diff --git a/setup.py b/setup.py
index 7962be9..338c7dc 100644
--- a/setup.py
+++ b/setup.py
@@ -8,7 +8,7 @@
 
 setup(
     name="pyvalem",
-    version="2.7.1",
+    version="2.8.0",
     description="A package for managing simple chemical species and states",
     long_description=long_description,
     long_description_content_type="text/x-rst",
@@ -29,6 +29,7 @@
         "Programming Language :: Python :: 3.10",
         "Programming Language :: Python :: 3.11",
         "Programming Language :: Python :: 3.12",
+        "Programming Language :: Python :: 3.13",
         "Programming Language :: Python :: 3 :: Only",
         "Operating System :: OS Independent",
     ],
diff --git a/src/pyvalem/stateful_species.py b/src/pyvalem/stateful_species.py
index ffb1325..4e9254a 100644
--- a/src/pyvalem/stateful_species.py
+++ b/src/pyvalem/stateful_species.py
@@ -29,7 +29,7 @@ def __init__(self, s):
 
         i = s.index(" ")
         self.formula = Formula(s[:i])
-        s = s.replace(";", " ").replace(",", " ")
+        s = s.replace(";", " ").replace(", ", " ")
         self.states = state_parser(s[i + 1 :].split())
 
         self._verify_states()
diff --git a/src/pyvalem/states/J1J2_coupling.py b/src/pyvalem/states/J1J2_coupling.py
new file mode 100644
index 0000000..1c89615
--- /dev/null
+++ b/src/pyvalem/states/J1J2_coupling.py
@@ -0,0 +1,102 @@
+"""
+The J1J2_Coupling class, representing a complex atomic state with two
+groups of separately spin-orbit coupled electrons giving rise to a
+(J1, J2) term symbol, perhaps further coupled to a total (J1, J2)_J
+level, with or without parity designator.
+
+W. C. Martin, W. Wiese, A. Kramida, "Atomic Spectroscopy" in "Springer
+Handbook of Atomic, Molecular and Optical Physics", G. W. F. Drake (ed.),
+https://doi.org/10.1007/978-3-030-73893-8_11
+
+Includes methods for parsing a string into quantum numbers and labels,
+creating an HTML representation of the term symbol, etc.
+"""
+
+import pyparsing as pp
+
+from pyvalem._utils import parse_fraction, float_to_fraction
+from pyvalem.states._base_state import State, StateParseError
+
+integer = pp.Word(pp.nums)
+J1str = (integer + pp.Optional(pp.Suppress("/") + "2")).setResultsName("J1str")
+J2str = (integer + pp.Optional(pp.Suppress("/") + "2")).setResultsName("J2str")
+Jstr = (integer + pp.Optional(pp.Suppress("/") + "2")).setResultsName("Jstr")
+parity = pp.Literal("o").setResultsName("parity")
+J1J2_term = (
+    "("
+    + J1str
+    + ","
+    + J2str
+    + ")"
+    + pp.Optional(parity)
+    + pp.Optional(pp.Suppress("_") + Jstr)
+    + pp.StringEnd()
+)
+
+
+class J1J2_CouplingError(StateParseError):
+    pass
+
+
+class J1J2_CouplingValidationError(ValueError):
+    pass
+
+
+class J1J2_Coupling(State):
+    def __init__(self, state_str):
+        self.state_str = state_str
+        self.J1 = None
+        self.J2 = None
+        self.parity = None
+        self.J = None
+        self._parse_state(state_str)
+
+    def _parse_state(self, state_str):
+        try:
+            components = J1J2_term.parseString(state_str)
+        except pp.ParseException:
+            raise J1J2_CouplingError(f"Invalid J1J2 coupling term syntax: {state_str}")
+        self.J1 = parse_fraction(components.J1str)
+        self.J2 = parse_fraction(components.J2str)
+        self.J = parse_fraction(components.get("Jstr"))
+        self.parity = components.get("parity")
+
+        if self.J is not None:
+            self._validate_J()
+
+    def _validate_J(self):
+        J1_is_half_integer = int(2 * self.J1) % 2
+        J2_is_half_integer = int(2 * self.J2) % 2
+        J_is_half_integer = int(2 * self.J) % 2
+        if (J1_is_half_integer == J2_is_half_integer) == J_is_half_integer:
+            raise J1J2_CouplingValidationError(
+                f"J={self.J} is invalid for J1={self.J1} and J2={self.J2}."
+            )
+        if not abs(self.J1 - self.J2) <= self.J <= self.J1 + self.J2:
+            raise J1J2_CouplingValidationError(
+                f"Invalid atomic term symbol: {self.state_str}"
+                f" |J1-J2| <= J <= J1+J2 must be satisfied."
+            )
+
+    @property
+    def html(self):
+        html_chunks = [f"({float_to_fraction(self.J1)}, {float_to_fraction(self.J2)})"]
+        if self.parity:
+            html_chunks.append("<sup>o</sup>")
+        if self.J is not None:
+            J_str = float_to_fraction(self.J)
+            html_chunks.append(f"<sub>{J_str}</sub>")
+        return "".join(html_chunks)
+
+    @property
+    def latex(self):
+        latex_chunks = [f"({float_to_fraction(self.J1)}, {float_to_fraction(self.J2)})"]
+        if self.parity:
+            latex_chunks.append("^o")
+        if self.J is not None:
+            J_str = float_to_fraction(self.J)
+            latex_chunks.append("_{{{}}}".format(J_str))
+        return "".join(latex_chunks)
+
+    def __repr__(self):
+        return self.state_str
diff --git a/src/pyvalem/states/__init__.py b/src/pyvalem/states/__init__.py
index c34eb0e..b84ec63 100644
--- a/src/pyvalem/states/__init__.py
+++ b/src/pyvalem/states/__init__.py
@@ -18,3 +18,4 @@
     J1K_LK_CouplingError,
     J1K_LK_CouplingValidationError,
 )
+from .J1J2_coupling import J1J2_Coupling, J1J2_CouplingError
diff --git a/src/pyvalem/states/_state_parser.py b/src/pyvalem/states/_state_parser.py
index 92f5244..1b1c446 100644
--- a/src/pyvalem/states/_state_parser.py
+++ b/src/pyvalem/states/_state_parser.py
@@ -16,6 +16,7 @@
 from .vibrational_state import VibrationalState
 from .compound_LS_coupling import CompoundLSCoupling
 from .J1K_LK_coupling import J1K_LK_Coupling
+from .J1J2_coupling import J1J2_Coupling
 
 # the following has two purposes: keys determine the order in which the
 # states are parsed, and the values determine the sorting order of states
@@ -29,6 +30,7 @@
         (DiatomicMolecularConfiguration, 1),
         (MolecularTermSymbol, 2),
         (J1K_LK_Coupling, 3),
+        (J1J2_Coupling, 3),
         (VibrationalState, 4),
         (RotationalState, 5),
         (RacahSymbol, 6),
diff --git a/tests/test_J1J2_coupling.py b/tests/test_J1J2_coupling.py
new file mode 100644
index 0000000..7efbba4
--- /dev/null
+++ b/tests/test_J1J2_coupling.py
@@ -0,0 +1,30 @@
+"""
+Unit tests for the J1J2_coupling module of PyValem.
+"""
+
+import unittest
+
+from pyvalem.states.J1J2_coupling import (
+    J1J2_Coupling,
+    J1J2_CouplingError,
+    J1J2_CouplingValidationError,
+)
+
+
+class J1J2_CouplingTest(unittest.TestCase):
+    def test_J1J2_coupling(self):
+        t0 = J1J2_Coupling("(1,3)")
+        self.assertEqual(t0.J1, 1)
+        self.assertEqual(t0.J2, 3)
+        self.assertIsNone(t0.J)
+
+        t1 = J1J2_Coupling("(2,3/2)o_1/2")
+        self.assertEqual(t1.J1, 2)
+        self.assertEqual(t1.J2, 1.5)
+        self.assertEqual(t1.J, 0.5)
+
+    def test_J_validation(self):
+        with self.assertRaises(J1J2_CouplingValidationError):
+            J1J2_Coupling("(1,1/2)_2")
+        with self.assertRaises(J1J2_CouplingValidationError):
+            J1J2_Coupling("(5/2,1/2)_1")
diff --git a/tests/test_compound_LS_coupling.py b/tests/test_compound_LS_coupling.py
index 0f4629e..e7e820e 100644
--- a/tests/test_compound_LS_coupling.py
+++ b/tests/test_compound_LS_coupling.py
@@ -54,3 +54,6 @@ def test_compound_LS_coupling(self):
         self.assertEqual(
             s3.html, """5p<sup>5</sup>(<sup>2</sup>P<sup>o</sup><sub>3/2</sub>)6d"""
         )
+
+        s4 = CompoundLSCoupling("4d9(2D_5/2)5s")
+        self.assertEqual(s4.html, """4d<sup>9</sup>(<sup>2</sup>D<sub>5/2</sub>)5s""")
diff --git a/tests/test_stateful_species.py b/tests/test_stateful_species.py
index de9b3a7..ab518ed 100644
--- a/tests/test_stateful_species.py
+++ b/tests/test_stateful_species.py
@@ -16,7 +16,7 @@ def test_stateful_species_parsing(self):
         _ = StatefulSpecies("Fe e5G")
         _ = StatefulSpecies("CrH 1sigma2.2sigma1.1pi4.3sigma1; 6SIGMA+")
         _ = StatefulSpecies("H(35Cl) J=2")
-        _ = StatefulSpecies("OH X(2Π_1/2, J=2")
+        _ = StatefulSpecies("OH X(2Π_1/2) J=2")
 
         _ = StatefulSpecies("HCl v=2 J=0")
         _ = StatefulSpecies("C2H3Cl")
@@ -57,7 +57,7 @@ def test_state_appears_at_most_once(self):
         self.assertRaises(StatefulSpeciesError, StatefulSpecies, "CO J=0; J=1")
         self.assertRaises(StatefulSpeciesError, StatefulSpecies, "CO X(1PIu);2Σ-")
         self.assertRaises(StatefulSpeciesError, StatefulSpecies, "Ar *;**")
-        self.assertRaises(StatefulSpeciesError, StatefulSpecies, "Ar 2S, 2P_3/2")
+        self.assertRaises(StatefulSpeciesError, StatefulSpecies, "Ar 2S 2P_3/2")
         # StatefulSpecies('CH3Cl J=2;Ka=1;Kc=2')
 
     def test_atomic_configuration_verification(self):
@@ -122,6 +122,8 @@ def test_compoundLScoupling_species(self):
 
         ss2 = StatefulSpecies("Fe+3 3d5(b2D)4s 3D_3")
 
+        ss3 = StatefulSpecies("Pd 4d9(2D_5/2)5s 2[5/2]")
+
     def test_incomplete_atomic_orbital_specification(self):
         ss1 = StatefulSpecies("Al 3s2.nd; y2D")
         self.assertEqual(ss1.html, "Al 3s<sup>2</sup><em>n</em>d y<sup>2</sup>D")
@@ -131,6 +133,10 @@ def test_J1K_LK_coupling(self):
         _ = StatefulSpecies("Ne+3 2s2.2p2(3P_2)5g 2[6]_11/2")
         _ = StatefulSpecies("Ne+3 2s2.2p2(3P_2)5g 2[6]")
 
+    def test_J1J2_coupling(self):
+        _ = StatefulSpecies("Pd 6s2.6p.7s (3/2,1/2)")
+        _ = StatefulSpecies("Bi 5d4.6s(6D)31d (1/2,3/2)o_2")
+
 
 if __name__ == "__main__":
     unittest.main()