diff --git a/src/scenic/core/external_params.py b/src/scenic/core/external_params.py
index 88848db4b..24cae6acf 100644
--- a/src/scenic/core/external_params.py
+++ b/src/scenic/core/external_params.py
@@ -96,6 +96,9 @@
 
 """
 
+from abc import ABC, abstractmethod
+import warnings
+
 from dotmap import DotMap
 import numpy
 
@@ -182,6 +185,7 @@ def __init__(self, params, globalParams):
         import verifai.server
 
         # construct FeatureSpace
+        timeBound = globalParams.get("timeBound", 0)
         usingProbs = False
         self.params = tuple(params)
         for index, param in enumerate(self.params):
@@ -193,11 +197,23 @@ def __init__(self, params, globalParams):
             param.index = index
             if param.probs is not None:
                 usingProbs = True
+
+        if timeBound == 0 and any(param.isTimeSeries for param in self.params):
+            warnings.warn(
+                "TimeSeries external parameter used but no global parameter `timeBound` is specified. "
+                "(If using VerifAI’s ScenicSampler, set its maxSteps option)."
+            )
+
         space = verifai.features.FeatureSpace(
             {
-                self.nameForParam(index): verifai.features.Feature(param.domain)
+                self.nameForParam(index): (
+                    verifai.features.Feature(param.domain)
+                    if not param.isTimeSeries
+                    else verifai.features.TimeSeriesFeature(param.domain)
+                )
                 for index, param in enumerate(self.params)
-            }
+            },
+            timeBound=timeBound,
         )
 
         # set up VerifAI sampler
@@ -252,17 +268,48 @@ def __init__(self, params, globalParams):
             self.rejectionFeedback = 1
         self.cachedSample = None
 
+        self._lastSample = None
+        self._lastDynamicSample = None
+        self._lastSimulation = None
+        self._lastTime = -1
+
     def nextSample(self, feedback):
-        return self.sampler.nextSample(feedback)
+        if feedback is not None:
+            assert self._lastSample is not None
+            self._lastSample.update(feedback)
 
-    def update(self, sample, info, rho):
-        self.sampler.update(sample, info, rho)
+        self._lastSample = self.sampler.getSample()
+        return self._lastSample
 
-    def getSample(self):
-        return self.sampler.getSample()
+    def nextDynamicSample(self):
+        import scenic.syntax.veneer as veneer
+
+        assert veneer.currentSimulation is not None
+
+        if self._lastSimulation is not veneer.currentSimulation:
+            self._lastSimulation = veneer.currentSimulation
+            self._lastTime = -1
+
+        if veneer.currentSimulation.currentTime > self._lastTime:
+            feedback = veneer.currentSimulation
+            self._lastDynamicSample = self.cachedSample.getDynamicSample(feedback)
+            self._lastTime = veneer.currentSimulation.currentTime
+
+        return self._lastDynamicSample
 
     def valueFor(self, param):
-        return getattr(self.cachedSample, self.nameForParam(param.index))
+        if not param.isTimeSeries:
+            return param.extractOutput(
+                getattr(self.cachedSample.staticSample, self.nameForParam(param.index))
+            )
+        else:
+            callback = lambda: param.extractOutput(
+                getattr(
+                    self.nextDynamicSample(),
+                    self.nameForParam(param.index),
+                )
+            )
+            return TimeSeriesParameter(callback)
 
     @staticmethod
     def nameForParam(i):
@@ -276,6 +323,7 @@ class ExternalParameter(Distribution):
     def __init__(self):
         super().__init__()
         self.sampler = None
+        self.isTimeSeries = False
         import scenic.syntax.veneer as veneer  # TODO improve?
 
         veneer.registerExternalParameter(self)
@@ -289,6 +337,41 @@ def sampleGiven(self, value):
         assert self.sampler is not None
         return self.sampler.valueFor(self)
 
+    def extractOutput(self, value):
+        """
+        Given a raw sampled value for a parameter, optionally extract the actual desired value.
+
+        By default just passes the value through unchanged.
+        """
+        return value
+
+
+class TimeSeriesParameter:
+    def __init__(self, callback):
+        self._callback = callback
+        self._lastTime = -1
+
+    def getSample(self):
+        import scenic.syntax.veneer as veneer
+
+        assert veneer.currentSimulation is not None
+
+        if veneer.currentSimulation.currentTime <= self._lastTime:
+            raise RuntimeError(
+                "Attempted `getSample` for a TimeSeries external parameter twice in one timestep."
+            )
+
+        self._lastTime = veneer.currentSimulation.currentTime
+        return self._callback()
+
+
+def TimeSeries(param):
+    if not isinstance(param, ExternalParameter):
+        raise TypeError("Cannot turn a non `ExternalParameter` into a time series")
+
+    param.isTimeSeries = True
+    return param
+
 
 class VerifaiParameter(ExternalParameter):
     """An external parameter sampled using one of VerifAI's samplers."""
@@ -341,8 +424,7 @@ def __init__(self, low, high, buckets=None, weights=None):
         total = sum(weights)
         self.probs = tuple(wt / total for wt in weights)
 
-    def sampleGiven(self, value):
-        value = super().sampleGiven(value)
+    def extractOutput(self, value):
         assert len(value) == 1
         return value[0]
 
@@ -367,8 +449,7 @@ def __init__(self, low, high, weights=None):
         else:
             self.probs = None
 
-    def sampleGiven(self, value):
-        value = super().sampleGiven(value)
+    def extractOutput(self, value):
         assert len(value) == 1
         return value[0]
 
diff --git a/src/scenic/syntax/veneer.py b/src/scenic/syntax/veneer.py
index cce52162f..034ff61d8 100644
--- a/src/scenic/syntax/veneer.py
+++ b/src/scenic/syntax/veneer.py
@@ -120,6 +120,7 @@
     "VerifaiRange",
     "VerifaiDiscreteRange",
     "VerifaiOptions",
+    "TimeSeries",
     "File",
     "Files",
     # Constructible types
@@ -201,6 +202,7 @@
 from scenic.core.dynamics.invocables import BlockConclusion, runTryInterrupt
 from scenic.core.dynamics.scenarios import DynamicScenario
 from scenic.core.external_params import (
+    TimeSeries,
     VerifaiDiscreteRange,
     VerifaiOptions,
     VerifaiParameter,