diff --git a/include/cantera/zeroD/ConstPressureReactor.h b/include/cantera/zeroD/ConstPressureReactor.h
index 445344434..4c5c896b3 100644
--- a/include/cantera/zeroD/ConstPressureReactor.h
+++ b/include/cantera/zeroD/ConstPressureReactor.h
@@ -43,6 +43,7 @@ public:
     //! the name of a homogeneous phase species, or the name of a surface
     //! species.
     virtual size_t componentIndex(const std::string& nm) const;
+    std::string componentName(size_t k);
 };
 
 }
diff --git a/include/cantera/zeroD/IdealGasConstPressureReactor.h b/include/cantera/zeroD/IdealGasConstPressureReactor.h
index 76f0accac..bdca2b36c 100644
--- a/include/cantera/zeroD/IdealGasConstPressureReactor.h
+++ b/include/cantera/zeroD/IdealGasConstPressureReactor.h
@@ -44,6 +44,7 @@ public:
     //! "temperature", the name of a homogeneous phase species, or the name of a
     //! surface species.
     virtual size_t componentIndex(const std::string& nm) const;
+    std::string componentName(size_t k);
 
 protected:
     vector_fp m_hk; //!< Species molar enthalpies
diff --git a/include/cantera/zeroD/IdealGasReactor.h b/include/cantera/zeroD/IdealGasReactor.h
index ca1f0f747..babd7518c 100644
--- a/include/cantera/zeroD/IdealGasReactor.h
+++ b/include/cantera/zeroD/IdealGasReactor.h
@@ -43,6 +43,7 @@ public:
     //! "volume", "temperature", the name of a homogeneous phase species, or the
     //! name of a surface species.
     virtual size_t componentIndex(const std::string& nm) const;
+    std::string componentName(size_t k);
 
 protected:
     vector_fp m_uk; //!< Species molar internal energies
diff --git a/include/cantera/zeroD/Reactor.h b/include/cantera/zeroD/Reactor.h
index cc2a43708..1c8e4f7d5 100644
--- a/include/cantera/zeroD/Reactor.h
+++ b/include/cantera/zeroD/Reactor.h
@@ -80,6 +80,9 @@ public:
 
     //! Number of equations (state variables) for this reactor
     virtual size_t neq() {
+        if (!m_nv) {
+            initialize();
+        }
         return m_nv;
     }
 
@@ -136,6 +139,10 @@ public:
     //! surface species.
     virtual size_t componentIndex(const std::string& nm) const;
 
+    //! Return the name of the solution component with index *i*.
+    //! @see componentIndex()
+    virtual std::string componentName(size_t k);
+
 protected:
     //! Set reaction rate multipliers based on the sensitivity variables in
     //! *params*.
diff --git a/include/cantera/zeroD/ReactorNet.h b/include/cantera/zeroD/ReactorNet.h
index 7dcb1bfab..e88a9a3c2 100644
--- a/include/cantera/zeroD/ReactorNet.h
+++ b/include/cantera/zeroD/ReactorNet.h
@@ -174,6 +174,11 @@ public:
     //! reactor network.
     size_t globalComponentIndex(const std::string& component, size_t reactor=0);
 
+    //! Return the name of the i-th component of the global state vector. The
+    //! name returned includes both the name of the reactor and the specific
+    //! component, e.g. `'reactor1: CH4'`.
+    std::string componentName(size_t i) const;
+
     //! Used by Reactor and Wall objects to register the addition of
     //! sensitivity parameters so that the ReactorNet can keep track of the
     //! order in which sensitivity parameters are added.
diff --git a/interfaces/cython/cantera/_cantera.pxd b/interfaces/cython/cantera/_cantera.pxd
index ae2528fb9..7e04cae5f 100644
--- a/interfaces/cython/cantera/_cantera.pxd
+++ b/interfaces/cython/cantera/_cantera.pxd
@@ -487,6 +487,7 @@ cdef extern from "cantera/zeroD/Reactor.h":
         void setEnergy(int)
         cbool energyEnabled()
         size_t componentIndex(string&)
+        string componentName(size_t) except +
         size_t neq()
         void getState(double*)
 
@@ -566,6 +567,7 @@ cdef extern from "cantera/zeroD/ReactorNet.h":
         void setVerbose(cbool)
         size_t neq()
         void getState(double*)
+        string componentName(size_t) except +
 
         void setSensitivityTolerances(double, double)
         double rtolSensitivity()
diff --git a/interfaces/cython/cantera/reactor.pyx b/interfaces/cython/cantera/reactor.pyx
index e02ad9e99..9e66284ff 100644
--- a/interfaces/cython/cantera/reactor.pyx
+++ b/interfaces/cython/cantera/reactor.pyx
@@ -233,9 +233,9 @@ cdef class Reactor(ReactorBase):
         """
         Returns the index of the component named *name* in the system. This
         determines the (relative) index of the component in the vector of
-        sensitivity coefficients. *name* is either a species name or the name
-        of a reactor state variable, e.g. 'U', 'T', depending on the reactor's
-        equations.
+        sensitivity coefficients. *name* is either a species name or the name of
+        a reactor state variable, e.g. 'int_energy', 'temperature', depending on
+        the reactor's equations.
         """
 
         k = self.reactor.componentIndex(stringify(name))
@@ -243,6 +243,14 @@ cdef class Reactor(ReactorBase):
             raise IndexError('No such component: {!r}'.format(name))
         return k
 
+    def component_name(self, int i):
+        """
+        Returns the name of the component with index *i* within the array of
+        variables returned by `get_state`. This is the inverse of
+        `component_index`.
+        """
+        return pystr(self.reactor.componentName(i))
+
     property n_vars:
         """
         The number of state variables in the reactor.
@@ -276,8 +284,9 @@ cdef class Reactor(ReactorBase):
           - 1  - enthalpy or temperature
           - 2+ - mass fractions of the species
 
-        You can use the function `component_index` to determine the location
-        of a specific component
+        You can use the function `component_index` to determine the location of
+        a specific component from its name, or `component_name` to determine the
+        name from the index.
         """
         if not self.n_vars:
             raise Exception('Reactor empty or network not initialized.')
@@ -908,6 +917,14 @@ cdef class ReactorNet:
         def __set__(self, pybool v):
             self.net.setVerbose(v)
 
+    def component_name(self, int i):
+        """
+        Return the name of the i-th component of the global state vector. The
+        name returned includes both the name of the reactor and the specific
+        component, e.g. `'reactor1: CH4'`.
+        """
+        return pystr(self.net.componentName(i))
+
     def sensitivity(self, component, int p, int r=0):
         """
         Returns the sensitivity of the solution variable *component* in
diff --git a/interfaces/cython/cantera/test/test_reactor.py b/interfaces/cython/cantera/test/test_reactor.py
index a34c298bc..1e4187bbc 100644
--- a/interfaces/cython/cantera/test/test_reactor.py
+++ b/interfaces/cython/cantera/test/test_reactor.py
@@ -83,6 +83,16 @@ class TestReactor(utilities.CanteraTest):
         for i, name in enumerate(self.gas1.species_names):
             self.assertEqual(i + N0, self.r1.component_index(name))
 
+    def test_component_names(self):
+        self.make_reactors(n_reactors=2)
+        N = self.net.n_vars // 2
+        for i in range(N):
+            self.assertEqual(self.r1.component_index(self.r1.component_name(i)), i)
+            self.assertEqual(self.net.component_name(i),
+                '{}: {}'.format(self.r1.name, self.r1.component_name(i)))
+            self.assertEqual(self.net.component_name(N+i),
+                '{}: {}'.format(self.r2.name, self.r2.component_name(i)))
+
     def test_disjoint(self):
         T1, P1 = 300, 101325
         T2, P2 = 500, 300000
@@ -757,6 +767,13 @@ class TestConstPressureReactor(utilities.CanteraTest):
             for i, name in enumerate(iface.species_names):
                 self.assertEqual(i + N1, r.component_index(name))
 
+    def test_component_names(self):
+        self.create_reactors(add_surf=True)
+        for i in range(self.net1.n_vars):
+            self.assertEqual(self.r1.component_index(self.r1.component_name(i)), i)
+            self.assertEqual(self.net1.component_name(i),
+                '{}: {}'.format(self.r1.name, self.r1.component_name(i)))
+
     def integrate(self, surf=False):
         for t in np.arange(0.5, 50, 1.0):
             self.net1.advance(t)
diff --git a/src/zeroD/ConstPressureReactor.cpp b/src/zeroD/ConstPressureReactor.cpp
index 171a1467c..9f16a037e 100644
--- a/src/zeroD/ConstPressureReactor.cpp
+++ b/src/zeroD/ConstPressureReactor.cpp
@@ -4,6 +4,7 @@
 
 #include "cantera/zeroD/ConstPressureReactor.h"
 #include "cantera/zeroD/FlowDevice.h"
+#include "cantera/zeroD/Wall.h"
 
 using namespace std;
 
@@ -149,4 +150,33 @@ size_t ConstPressureReactor::componentIndex(const string& nm) const
     }
 }
 
+std::string ConstPressureReactor::componentName(size_t k) {
+    if (k == 0) {
+        return "mass";
+    } else if (k == 1) {
+        return "enthalpy";
+    } else if (k >= 2 && k < neq()) {
+        k -= 2;
+        if (k < m_thermo->nSpecies()) {
+            return m_thermo->speciesName(k);
+        } else {
+            k -= m_thermo->nSpecies();
+        }
+        for (size_t m = 0; m < m_wall.size(); m++) {
+            Wall& w = *m_wall[m];
+            if (w.kinetics(m_lr[m])) {
+                size_t kp = w.kinetics(m_lr[m])->reactionPhaseIndex();
+                ThermoPhase& th = w.kinetics(m_lr[m])->thermo(kp);
+                if (k < th.nSpecies()) {
+                    return th.speciesName(k);
+                } else {
+                    k -= th.nSpecies();
+                }
+            }
+        }
+    }
+    throw CanteraError("ConstPressureReactor::componentName",
+                       "Index is out of bounds.");
+}
+
 }
diff --git a/src/zeroD/IdealGasConstPressureReactor.cpp b/src/zeroD/IdealGasConstPressureReactor.cpp
index 6df0b9dd9..480ceeaa2 100644
--- a/src/zeroD/IdealGasConstPressureReactor.cpp
+++ b/src/zeroD/IdealGasConstPressureReactor.cpp
@@ -161,4 +161,12 @@ size_t IdealGasConstPressureReactor::componentIndex(const string& nm) const
     }
 }
 
+std::string IdealGasConstPressureReactor::componentName(size_t k) {
+    if (k == 1) {
+        return "temperature";
+    } else {
+        return ConstPressureReactor::componentName(k);
+    }
+}
+
 }
diff --git a/src/zeroD/IdealGasReactor.cpp b/src/zeroD/IdealGasReactor.cpp
index 4f7064bb8..5c2b9fa3b 100644
--- a/src/zeroD/IdealGasReactor.cpp
+++ b/src/zeroD/IdealGasReactor.cpp
@@ -176,4 +176,13 @@ size_t IdealGasReactor::componentIndex(const string& nm) const
     }
 }
 
+std::string IdealGasReactor::componentName(size_t k) {
+    if (k == 2) {
+        return "temperature";
+    } else {
+        return Reactor::componentName(k);
+    }
+}
+
+
 }
diff --git a/src/zeroD/Reactor.cpp b/src/zeroD/Reactor.cpp
index 49db701a6..3917a96eb 100644
--- a/src/zeroD/Reactor.cpp
+++ b/src/zeroD/Reactor.cpp
@@ -398,6 +398,36 @@ size_t Reactor::componentIndex(const string& nm) const
     }
 }
 
+std::string Reactor::componentName(size_t k) {
+    if (k == 0) {
+        return "mass";
+    } else if (k == 1) {
+        return "volume";
+    } else if (k == 2) {
+        return "int_energy";
+    } else if (k >= 3 && k < neq()) {
+        k -= 3;
+        if (k < m_thermo->nSpecies()) {
+            return m_thermo->speciesName(k);
+        } else {
+            k -= m_thermo->nSpecies();
+        }
+        for (size_t m = 0; m < m_wall.size(); m++) {
+            Wall& w = *m_wall[m];
+            if (w.kinetics(m_lr[m])) {
+                size_t kp = w.kinetics(m_lr[m])->reactionPhaseIndex();
+                ThermoPhase& th = w.kinetics(m_lr[m])->thermo(kp);
+                if (k < th.nSpecies()) {
+                    return th.speciesName(k);
+                } else {
+                    k -= th.nSpecies();
+                }
+            }
+        }
+    }
+    throw CanteraError("Reactor::componentName", "Index is out of bounds.");
+}
+
 void Reactor::applySensitivity(double* params)
 {
     if (!params) {
diff --git a/src/zeroD/ReactorNet.cpp b/src/zeroD/ReactorNet.cpp
index adc790f66..f7c78bfe9 100644
--- a/src/zeroD/ReactorNet.cpp
+++ b/src/zeroD/ReactorNet.cpp
@@ -242,6 +242,18 @@ size_t ReactorNet::globalComponentIndex(const string& component, size_t reactor)
     return m_start[reactor] + m_reactors[reactor]->componentIndex(component);
 }
 
+std::string ReactorNet::componentName(size_t i) const
+{
+    for (auto r : m_reactors) {
+        if (i < r->neq()) {
+            return r->name() + ": " + r->componentName(i);
+        } else {
+            i -= r->neq();
+        }
+    }
+    throw CanteraError("ReactorNet::componentName", "Index out of bounds");
+}
+
 size_t ReactorNet::registerSensitivityParameter(
     const std::string& name, double value, double scale)
 {