diff --git a/haystack/core/pipeline/base.py b/haystack/core/pipeline/base.py
index d8f2a65932..9a84eb6e13 100644
--- a/haystack/core/pipeline/base.py
+++ b/haystack/core/pipeline/base.py
@@ -1209,27 +1209,34 @@ def _break_supported_cycles_in_graph(self) -> Tuple[networkx.MultiDiGraph, Dict[
             # sender_comp will be the last element of cycle and receiver_comp will be the first.
             # So if cycle is [1, 2, 3, 4] we would call zip([1, 2, 3, 4], [2, 3, 4, 1]).
             for sender_comp, receiver_comp in zip(cycle, cycle[1:] + cycle[:1]):
-                # We get the key and iterate those as we want to edit the graph data while
-                # iterating the edges and that would raise.
-                # Even though the connection key set in Pipeline.connect() uses only the
-                # sockets name we don't have clashes since it's only used to differentiate
-                # multiple edges between two nodes.
-                edge_keys = list(temp_graph.get_edge_data(sender_comp, receiver_comp).keys())
-                for edge_key in edge_keys:
-                    edge_data = temp_graph.get_edge_data(sender_comp, receiver_comp)[edge_key]
-                    receiver_socket = edge_data["to_socket"]
-                    if not receiver_socket.is_variadic and receiver_socket.is_mandatory:
-                        continue
-
-                    # We found a breakable edge
-                    sender_socket = edge_data["from_socket"]
-                    edges_removed[sender_comp].append(sender_socket.name)
-                    temp_graph.remove_edge(sender_comp, receiver_comp, edge_key)
-
-                    graph_has_cycles = not networkx.is_directed_acyclic_graph(temp_graph)
-                    if not graph_has_cycles:
-                        # We removed all the cycles, we can stop
-                        break
+                # for graphs with multiple nested cycles, we need to check if the edge hasn't
+                # been previously removed before we try to remove it again
+                edge_data = temp_graph.get_edge_data(sender_comp, receiver_comp)
+                if edge_data is not None:
+                    # We get the key and iterate those as we want to edit the graph data while
+                    # iterating the edges and that would raise.
+                    # Even though the connection key set in Pipeline.connect() uses only the
+                    # sockets name we don't have clashes since it's only used to differentiate
+                    # multiple edges between two nodes.
+                    edge_keys = list(edge_data.keys())
+
+                    for edge_key in edge_keys:
+                        edge_data = temp_graph.get_edge_data(sender_comp, receiver_comp)[edge_key]
+                        receiver_socket = edge_data["to_socket"]
+                        if not receiver_socket.is_variadic and receiver_socket.is_mandatory:
+                            continue
+
+                        # We found a breakable edge
+                        sender_socket = edge_data["from_socket"]
+                        edges_removed[sender_comp].append(sender_socket.name)
+                        temp_graph.remove_edge(sender_comp, receiver_comp, edge_key)
+
+                        # The following check seems heavy, considering there are more cycles to iterate on,
+                        # although in some cases I can see that breaking one edge might break more than one cycle
+                        graph_has_cycles = not networkx.is_directed_acyclic_graph(temp_graph)
+                        if not graph_has_cycles:
+                            # We removed all the cycles, we can stop
+                            break
 
             if not graph_has_cycles:
                 # We removed all the cycles, nice
diff --git a/releasenotes/notes/fix-break-sypported-cycles-in-grapth-f8769351fe4ca706.yaml b/releasenotes/notes/fix-break-sypported-cycles-in-grapth-f8769351fe4ca706.yaml
new file mode 100644
index 0000000000..fca7114249
--- /dev/null
+++ b/releasenotes/notes/fix-break-sypported-cycles-in-grapth-f8769351fe4ca706.yaml
@@ -0,0 +1,4 @@
+---
+fixes:
+  - |
+    Prevents the pipeline from raising an exception when there are multiple nested cycles in the graph.
diff --git a/test/core/pipeline/test_pipeline.py b/test/core/pipeline/test_pipeline.py
index 1cd57a5b5b..2bde85d050 100644
--- a/test/core/pipeline/test_pipeline.py
+++ b/test/core/pipeline/test_pipeline.py
@@ -1581,3 +1581,28 @@ def test__find_receivers_from(self):
                 ),
             )
         ]
+
+    def test__break_supported_cycles_in_graph(self):
+        # the following pipeline has a nested cycle, which is supported by Haystack
+        # but was causing an exception to be raised in the _break_supported_cycles_in_graph method
+        comp1 = component_class("Comp1", input_types={"value": int}, output_types={"value": int})()
+        comp2 = component_class("Comp2", input_types={"value": Variadic[int]}, output_types={"value": int})()
+        comp3 = component_class("Comp3", input_types={"value": Variadic[int]}, output_types={"value": int})()
+        comp4 = component_class("Comp4", input_types={"value": Optional[int]}, output_types={"value": int})()
+        comp5 = component_class("Comp5", input_types={"value": Variadic[int]}, output_types={"value": int})()
+        pipe = Pipeline()
+        pipe.add_component("comp1", comp1)
+        pipe.add_component("comp2", comp2)
+        pipe.add_component("comp3", comp3)
+        pipe.add_component("comp4", comp4)
+        pipe.add_component("comp5", comp5)
+        pipe.connect("comp1.value", "comp2.value")
+        pipe.connect("comp2.value", "comp3.value")
+        pipe.connect("comp3.value", "comp4.value")
+        pipe.connect("comp3.value", "comp5.value")
+        pipe.connect("comp4.value", "comp5.value")
+        pipe.connect("comp4.value", "comp3.value")
+        pipe.connect("comp5.value", "comp2.value")
+
+        # the following call should not raise an exception
+        pipe._break_supported_cycles_in_graph()