diff --git a/haystack/core/pipeline/pipeline.py b/haystack/core/pipeline/pipeline.py
index 73dbe59dc..2b8708b49 100644
--- a/haystack/core/pipeline/pipeline.py
+++ b/haystack/core/pipeline/pipeline.py
@@ -17,6 +17,7 @@ from haystack.core.errors import (
     PipelineConnectError,
     PipelineDrawingError,
     PipelineError,
+    PipelineMaxLoops,
     PipelineRuntimeError,
     PipelineValidationError,
 )
@@ -661,6 +662,10 @@ class Pipeline:
         #     "input1": 1, "input2": 2,
         # }
 
+        # Reset the visits count for each component
+        for node in self.graph.nodes:
+            self.graph.nodes[node]["visits"] = 0
+
         # TODO: Remove this warmup once we can check reliably whether a component has been warmed up or not
         # As of now it's here to make sure we don't have failing tests that assume warm_up() is called in run()
         self.warm_up()
@@ -759,8 +764,12 @@ class Pipeline:
                     continue
 
             if name in last_inputs and len(comp.__haystack_input__._sockets_dict) == len(last_inputs[name]):  # type: ignore
+                if self.graph.nodes[name]["visits"] > self.max_loops_allowed:
+                    msg = f"Maximum loops count ({self.max_loops_allowed}) exceeded for component '{name}'"
+                    raise PipelineMaxLoops(msg)
                 # This component has all the inputs it needs to run
                 res = comp.run(**last_inputs[name])
+                self.graph.nodes[name]["visits"] += 1
 
                 if not isinstance(res, Mapping):
                     raise PipelineRuntimeError(
diff --git a/releasenotes/notes/max-loops-in-run-df9f5c068a723f71.yaml b/releasenotes/notes/max-loops-in-run-df9f5c068a723f71.yaml
new file mode 100644
index 000000000..00c6d3a5d
--- /dev/null
+++ b/releasenotes/notes/max-loops-in-run-df9f5c068a723f71.yaml
@@ -0,0 +1,5 @@
+---
+enhancements:
+  - |
+    Change `Pipeline.run()` to check if `max_loops_allowed` has been reached.
+    If we attempt to run a Component that already ran the number of `max_loops_allowed` a `PipelineMaxLoops` will be raised.
diff --git a/test/core/pipeline/test_pipeline.py b/test/core/pipeline/test_pipeline.py
index 1876ee28b..d3690855a 100644
--- a/test/core/pipeline/test_pipeline.py
+++ b/test/core/pipeline/test_pipeline.py
@@ -9,7 +9,7 @@ import pytest
 
 from haystack.core.component import component
 from haystack.core.component.types import InputSocket, OutputSocket
-from haystack.core.errors import PipelineDrawingError, PipelineError, PipelineRuntimeError
+from haystack.core.errors import PipelineDrawingError, PipelineError, PipelineMaxLoops, PipelineRuntimeError
 from haystack.core.pipeline import Pipeline
 from haystack.testing.factory import component_class
 from haystack.testing.sample_components import AddFixedValue, Double
@@ -280,6 +280,22 @@ def test_repr_in_notebook(mock_is_in_jupyter):
         mock_show.assert_called_once_with()
 
 
+def test_run_raises_if_max_visits_reached():
+    def custom_init(self):
+        component.set_input_type(self, "x", int)
+        component.set_input_type(self, "y", int, 1)
+        component.set_output_types(self, a=int, b=int)
+
+    FakeComponent = component_class("FakeComponent", output={"a": 1, "b": 1}, extra_fields={"__init__": custom_init})
+    pipe = Pipeline(max_loops_allowed=1)
+    pipe.add_component("first", FakeComponent())
+    pipe.add_component("second", FakeComponent())
+    pipe.connect("first.a", "second.x")
+    pipe.connect("second.b", "first.y")
+    with pytest.raises(PipelineMaxLoops):
+        pipe.run({"first": {"x": 1}})
+
+
 def test_run_with_component_that_does_not_return_dict():
     BrokenComponent = component_class(
         "BrokenComponent", input_types={"a": int}, output_types={"b": int}, output=1  # type:ignore