diff --git a/qiskit_experiments/framework/composite/parallel_experiment.py b/qiskit_experiments/framework/composite/parallel_experiment.py
index bf384cda96..67f398c90e 100644
--- a/qiskit_experiments/framework/composite/parallel_experiment.py
+++ b/qiskit_experiments/framework/composite/parallel_experiment.py
@@ -16,7 +16,7 @@
 import numpy as np
 
 from qiskit import QuantumCircuit, ClassicalRegister
-from qiskit.circuit import Clbit
+from qiskit.circuit import Clbit, Delay
 from qiskit.providers.backend import Backend
 from qiskit_experiments.exceptions import QiskitError
 from .composite_experiment import CompositeExperiment, BaseExperiment
@@ -92,12 +92,39 @@ def _combined_circuits(self, device_layout: bool) -> List[QuantumCircuit]:
             else:
                 num_qubits = 1 + max(self.physical_qubits)
 
-        joint_circuits = []
-        sub_qubits = 0
+        # Transpile component circuits
+        transpiled_circuits = []
+
+        # Max duration for all components that will be combined into a single circuit
+        max_durations = {}
+        duration_unit = None
+        scheduling_method = getattr(self.transpile_options, "scheduling_method", None)
+
+        # Find max durations of subcircuits
         for exp_idx, sub_exp in enumerate(self._experiments):
             # Generate transpiled subcircuits
             sub_circuits = sub_exp._transpiled_circuits()
-
+            transpiled_circuits.append(sub_circuits)
+            if scheduling_method is not None:
+                for circ_idx, sub_circ in enumerate(sub_circuits):
+                    if sub_circ.duration is not None:
+                        if duration_unit is None:
+                            duration_unit = sub_circ.unit
+                        if circ_idx not in max_durations:
+                            max_durations[circ_idx] = 0
+                        max_durations[circ_idx] = max(sub_circ.duration, max_durations[circ_idx])
+                        if duration_unit != sub_circ.unit:
+                            raise QiskitError(
+                                "Scheduled component experiments are scheduled with"
+                                " different time units."
+                            )
+
+        # Combine circuits
+        joint_circuits = []
+        sub_qubits = 0
+        for exp_idx, (sub_circuits, sub_exp) in enumerate(
+            zip(transpiled_circuits, self._experiments)
+        ):
             # Qubit remapping for non-transpiled circuits
             if not device_layout:
                 qubits = list(range(sub_qubits, sub_qubits + sub_exp.num_qubits))
@@ -136,6 +163,18 @@ def _combined_circuits(self, device_layout: bool) -> List[QuantumCircuit]:
                 # Apply transpiled subcircuit
                 # Note that this assumes the circuit was not expanded to use
                 # any qubits outside the specified physical qubits
+                circ_duration = max_durations.get(circ_idx)
+                pad_time = None
+                if scheduling_method and sub_circ.duration and circ_duration:
+                    pad_time = abs(circ_duration - sub_circ.duration)
+
+                # If scheduling method is alap prepend shorter sub-circuits with delays
+                if scheduling_method == "alap" and pad_time:
+                    for i in sub_exp.physical_qubits:
+                        circuit._append(
+                            Delay(pad_time, unit=duration_unit), [circuit.qubits[i]], []
+                        )
+
                 for inst, qargs, cargs in sub_circ.data:
                     mapped_cargs = [sub_cargs[sub_circ.find_bit(i).index] for i in cargs]
                     try:
@@ -158,6 +197,18 @@ def _combined_circuits(self, device_layout: bool) -> List[QuantumCircuit]:
                         ) from ex
                     circuit._append(inst, mapped_qargs, mapped_cargs)
 
+                # If scheduling method is alap append shorter sub-circuits with delays
+                if scheduling_method == "asap" and pad_time:
+                    for i in sub_exp.physical_qubits:
+                        circuit._append(
+                            Delay(pad_time, unit=duration_unit), [circuit.qubits[i]], []
+                        )
+
+                # Update duration of circuit
+                if scheduling_method and circ_duration:
+                    circuit.duration = circ_duration
+                    circuit.unit = duration_unit
+
                 # Add subcircuit metadata
                 circuit.metadata["composite_index"].append(exp_idx)
                 circuit.metadata["composite_metadata"].append(sub_circ.metadata)
diff --git a/releasenotes/notes/parallel-scheduling-03e2eca55f8d8ff2.yaml b/releasenotes/notes/parallel-scheduling-03e2eca55f8d8ff2.yaml
new file mode 100644
index 0000000000..83f9ee1c66
--- /dev/null
+++ b/releasenotes/notes/parallel-scheduling-03e2eca55f8d8ff2.yaml
@@ -0,0 +1,7 @@
+---
+fixes:
+  - |
+    Fixes :class:`.ParallelExperiment` handling of `scheduling_method`
+    transpile option for `"asap"` and `"alap"` scheduling to correctly
+    pad the component experiment subcircuits so that the combined circuit
+    has a fixed duration on the experiments physical qubits.
diff --git a/test/library/characterization/test_t1.py b/test/library/characterization/test_t1.py
index fefab78329..16a46a8336 100644
--- a/test/library/characterization/test_t1.py
+++ b/test/library/characterization/test_t1.py
@@ -351,14 +351,14 @@ def test_t1_parallel_exp_transpile(self):
             self.assertEqual(circ.num_qubits, 2)
             op_counts = circ.count_ops()
             self.assertEqual(op_counts.get("rx"), 2)
-            self.assertEqual(op_counts.get("delay"), 2)
+            self.assertEqual(op_counts.get("delay"), 3)
 
         tcircs = parexp._transpiled_circuits()
         for circ in tcircs:
             self.assertEqual(circ.num_qubits, num_qubits)
             op_counts = circ.count_ops()
             self.assertEqual(op_counts.get("rx"), 2)
-            self.assertEqual(op_counts.get("delay"), 2)
+            self.assertEqual(op_counts.get("delay"), 3)
 
     def test_experiment_config(self):
         """Test converting to and from config works"""