diff --git a/pytket/tests/clexpr_test.py b/pytket/tests/clexpr_test.py
index e078224aa0..a585961cf4 100644
--- a/pytket/tests/clexpr_test.py
+++ b/pytket/tests/clexpr_test.py
@@ -12,6 +12,9 @@
 # See the License for the specific language governing permissions and
 # limitations under the License.
 
+import json
+from jsonschema import validate  # type: ignore
+from pathlib import Path
 from pytket.circuit import (
     Bit,
     CircBox,
@@ -21,11 +24,15 @@
     ClExprOp,
     ClOp,
     ClRegVar,
-    OpType,
     WiredClExpr,
 )
 from pytket.qasm import circuit_to_qasm_str, circuit_from_qasm_str
 
+with open(
+    Path(__file__).resolve().parent.parent.parent / "schemas/circuit_v1.json", "r"
+) as f:
+    SCHEMA = json.load(f)
+
 
 def test_op() -> None:
     reg_add = ClOp.RegAdd
@@ -114,16 +121,25 @@ def test_wexpr() -> None:
 
 
 def test_adding_to_circuit() -> None:
-    expr = ClExpr(op=ClOp.BitXor, args=[ClBitVar(0), ClBitVar(1)])
-    wexpr = WiredClExpr(expr=expr, bit_posn={0: 0, 1: 1}, output_posn=[2])
+    expr0 = ClExpr(op=ClOp.BitXor, args=[ClBitVar(0), ClBitVar(1)])
+    wexpr0 = WiredClExpr(expr=expr0, bit_posn={0: 0, 1: 1}, output_posn=[2])
+    expr1 = ClExpr(
+        op=ClOp.RegDiv,
+        args=[ClRegVar(0), ClExpr(op=ClOp.RegAdd, args=[2, ClBitVar(0)])],
+    )
+    wexpr1 = WiredClExpr(
+        expr=expr1, bit_posn={0: 1}, reg_posn={0: [2, 0]}, output_posn=[2, 0]
+    )
     c = Circuit(0, 3)
-    c.add_clexpr(wexpr, c.bits)
+    c.add_clexpr(wexpr0, c.bits)
+    c.add_clexpr(wexpr1, c.bits)
     cmds = c.get_commands()
-    assert len(cmds) == 1
+    assert len(cmds) == 2
     op = cmds[0].op
     assert isinstance(op, ClExprOp)
-    assert op.expr == wexpr
+    assert op.expr == wexpr0
     d = c.to_dict()
+    validate(instance=d, schema=SCHEMA)
     c1 = Circuit.from_dict(d)
     assert c == c1
     d1 = c1.to_dict()
diff --git a/schemas/circuit_v1.json b/schemas/circuit_v1.json
index c801393fbd..d788e573d3 100644
--- a/schemas/circuit_v1.json
+++ b/schemas/circuit_v1.json
@@ -302,6 +302,9 @@
         },
         "classical": {
           "$ref": "#/definitions/classical"
+        },
+        "expr": {
+          "$ref": "#/definitions/wiredclexpr"
         }
       },
       "required": [
@@ -357,6 +360,20 @@
               "classical"
             ]
           }
+        },
+        {
+          "if": {
+            "properties": {
+              "type": {
+                "const": "ClExpr"
+              }
+            }
+          },
+          "then": {
+            "required": [
+              "expr"
+            ]
+          }
         }
       ]
     },
@@ -1178,6 +1195,147 @@
         "qubits"
       ],
       "additionalProperties": false
+    },
+    "wiredclexpr": {
+      "type": "object",
+      "description": "A classical operation defined over a sequence of bits.",
+      "properties": {
+        "expr": {
+          "$ref": "#/definitions/clexpr"
+        },
+        "bit_posn": {
+          "type": "array",
+          "description": "List of pairs representing map from bit-variable indices to wire positions.",
+          "items": {
+            "type": "array",
+            "items": {
+              "type": "integer"
+            }
+          }
+        },
+        "reg_posn": {
+          "type": "array",
+          "description": "List of pairs representing map from register-variable indices to lists of wire positions.",
+          "items": {
+            "type": "array",
+            "items": [
+              {
+                "type": "integer"
+              },
+              {
+                "type": "array",
+                "items": {
+                  "type": "integer"
+                }
+              }
+            ]
+          }
+        },
+        "output_posn": {
+          "type": "array",
+          "description": "List of wire positions of output bits.",
+          "items": {
+            "type": "integer"
+          }
+        }
+      },
+      "required": [
+        "expr",
+        "bit_posn",
+        "reg_posn",
+        "output_posn"
+      ],
+      "additionalProperties": false
+    },
+    "clexpr": {
+      "type": "object",
+      "description": "An abstract classical expression.",
+      "properties": {
+        "op": {
+          "description": "The operation type.",
+          "type": "string"
+        },
+        "args": {
+          "type": "array",
+          "description": "List of arguments to the operation.",
+          "items": {
+            "$ref": "#/definitions/clexprarg"
+          }
+        }
+      }
+    },
+    "clexprarg":{
+      "type": "object",
+      "description": "Argument to a classical expression.",
+      "properties": {
+        "type": {
+          "description": "The type of argument.",
+          "type": "string",
+          "enum": [
+            "term",
+            "expr"
+          ]
+        },
+        "input": {
+          "anyOf": [
+            {
+              "$ref": "#/definitions/clexprterm"
+            },
+            {
+              "$ref": "#/definitions/clexpr"
+            }
+          ]
+        }
+      }
+    },
+    "clexprterm": {
+      "type": "object",
+      "description": "A term in a classical expression.",
+      "properties": {
+        "type": {
+          "description": "The type of term.",
+          "type": "string",
+          "enum": [
+            "int",
+            "var"
+          ]
+        },
+        "term": {
+          "anyOf": [
+            {
+              "type": "integer"
+            },
+            {
+              "$ref": "#/definitions/clvar"
+            }
+          ]
+        }
+      }
+    },
+    "clvar": {
+      "type": "object",
+      "description": "A free variable in a classical expression.",
+      "properties": {
+        "type": {
+          "description": "The type of variable.",
+          "type": "string",
+          "enum": [
+            "bit",
+            "ref"
+          ]
+        },
+        "var": {
+          "$ref": "#/definitions/clindex"
+        }
+      }
+    },
+    "clindex": {
+      "type": "object",
+      "properties": {
+        "index": {
+          "type": "integer"
+        }
+      }
     }
   }
 }