diff --git a/src/conductor/duration.py b/src/conductor/duration.py
index 1f70d377..4f12560e 100644
--- a/src/conductor/duration.py
+++ b/src/conductor/duration.py
@@ -14,6 +14,7 @@
 
 from __future__ import annotations
 
+import math
 import re
 
 _DURATION_PATTERN = re.compile(r"^\s*(?P<value>\d+(?:\.\d+)?)\s*(?P<unit>ms|s|m|h)?\s*$")
@@ -64,6 +65,8 @@ def parse_duration(value: str | int | float) -> float:
         raise ValueError(f"duration must be a number or duration string, not boolean: {value!r}")
 
     if isinstance(value, (int, float)):
+        if not math.isfinite(value):
+            raise ValueError(f"duration must be finite, got {value!r}")
         return float(value)
 
     if not isinstance(value, str):
@@ -79,5 +82,7 @@ def parse_duration(value: str | int | float) -> float:
         )
 
     number = float(match.group("value"))
+    if not math.isfinite(number):
+        raise ValueError(f"duration must be finite, got {value!r}")
     unit = match.group("unit") or "s"
     return number * _UNIT_TO_SECONDS[unit]
diff --git a/tests/test_engine/test_duration.py b/tests/test_engine/test_duration.py
index ce0038c8..7d4cb2a6 100644
--- a/tests/test_engine/test_duration.py
+++ b/tests/test_engine/test_duration.py
@@ -6,6 +6,8 @@
 
 from __future__ import annotations
 
+import math
+
 import pytest
 
 from conductor.duration import parse_duration
@@ -118,3 +120,12 @@ def test_list(self) -> None:
     def test_number_then_garbage(self) -> None:
         with pytest.raises(ValueError):
             parse_duration("5 minutes")
+
+    @pytest.mark.parametrize("value", [math.nan, math.inf, -math.inf])
+    def test_nonfinite_number(self, value: float) -> None:
+        with pytest.raises(ValueError, match="finite"):
+            parse_duration(value)
+
+    def test_overflowing_string_number(self) -> None:
+        with pytest.raises(ValueError, match="finite"):
+            parse_duration("9" * 400)