diff --git a/haystack/core/pipeline/pipeline.py b/haystack/core/pipeline/pipeline.py
index 9a61b70dd..ca3c683b9 100644
--- a/haystack/core/pipeline/pipeline.py
+++ b/haystack/core/pipeline/pipeline.py
@@ -846,6 +846,7 @@ class Pipeline:
                     ) as span:
                         span.set_content_tag("haystack.component.input", last_inputs[name])
 
+                        logger.info("Running component {name}", name=name)
                         res = comp.run(**last_inputs[name])
                         self.graph.nodes[name]["visits"] += 1
 
@@ -959,6 +960,15 @@ class Pipeline:
                         # There was a lazy variadic or a component with only default waiting for input, we can run it
                         waiting_for_input.remove((name, comp))
                         to_run.append((name, comp))
+
+                        # Let's use the default value for the inputs that are still missing, or the component
+                        # won't run and will be put back in the waiting list, causing an infinite loop.
+                        for input_socket in comp.__haystack_input__._sockets_dict.values():  # type: ignore
+                            if input_socket.is_mandatory:
+                                continue
+                            if input_socket.name not in last_inputs[name]:
+                                last_inputs[name][input_socket.name] = input_socket.default_value
+
                         continue
 
                     before_last_waiting_for_input = (
diff --git a/releasenotes/notes/fix-pipeline-run-loop-99f7ff9db16544d4.yaml b/releasenotes/notes/fix-pipeline-run-loop-99f7ff9db16544d4.yaml
new file mode 100644
index 000000000..61ad81c78
--- /dev/null
+++ b/releasenotes/notes/fix-pipeline-run-loop-99f7ff9db16544d4.yaml
@@ -0,0 +1,4 @@
+---
+fixes:
+  - |
+    Fix a bug when running a Pipeline that would cause it to get stuck in an infinite loop
diff --git a/test/core/pipeline/test_pipeline.py b/test/core/pipeline/test_pipeline.py
index 95dae8151..1e34a9292 100644
--- a/test/core/pipeline/test_pipeline.py
+++ b/test/core/pipeline/test_pipeline.py
@@ -2,7 +2,7 @@
 #
 # SPDX-License-Identifier: Apache-2.0
 import logging
-from typing import List, Optional
+from typing import Any, Dict, List, Optional
 from unittest.mock import patch
 
 import pytest
@@ -12,6 +12,7 @@ from haystack.components.builders import PromptBuilder
 from haystack.components.builders.answer_builder import AnswerBuilder
 from haystack.components.others import Multiplexer
 from haystack.components.retrievers.in_memory import InMemoryBM25Retriever
+from haystack.components.routers import ConditionalRouter
 from haystack.core.component import component
 from haystack.core.component.types import InputSocket, OutputSocket
 from haystack.core.errors import PipelineDrawingError, PipelineError, PipelineMaxLoops, PipelineRuntimeError
@@ -916,3 +917,69 @@ def test_pipeline_is_not_stuck_with_components_with_only_defaults():
     answers = res["answer_builder"]["answers"]
     assert len(answers) == 1
     assert answers[0].data == "Paris"
+
+
+def test_pipeline_is_not_stuck_with_components_with_only_defaults_as_first_components():
+    """
+    This tests verifies that a Pipeline doesn't get stuck running in a loop if
+    it has all the following characterics:
+    - The first Component has all defaults for its inputs
+    - The first Component receives one input from the user
+    - The first Component receives one input from a loop in the Pipeline
+    - The second Component has at least one default input
+    """
+
+    def fake_generator_run(self, prompt: str, generation_kwargs: Optional[Dict[str, Any]] = None):
+        # Simple hack to simulate a model returning a different reply after the
+        # the first time it's called
+        if getattr(fake_generator_run, "called", False):
+            return {"replies": ["Rome"]}
+        fake_generator_run.called = True
+        return {"replies": ["Paris"]}
+
+    FakeGenerator = component_class(
+        "FakeGenerator",
+        input_types={"prompt": str, "generation_kwargs": Optional[Dict[str, Any]]},
+        output_types={"replies": List[str]},
+        extra_fields={"run": fake_generator_run},
+    )
+    template = (
+        "Answer the following question.\n"
+        "{% if previous_replies %}\n"
+        "Previously you replied incorrectly this:\n"
+        "{% for reply in previous_replies %}\n"
+        " - {{ reply }}\n"
+        "{% endfor %}\n"
+        "{% endif %}\n"
+        "Question: {{ query }}"
+    )
+    router = ConditionalRouter(
+        routes=[
+            {
+                "condition": "{{ replies == ['Rome'] }}",
+                "output": "{{ replies }}",
+                "output_name": "correct_replies",
+                "output_type": List[int],
+            },
+            {
+                "condition": "{{ replies == ['Paris'] }}",
+                "output": "{{ replies }}",
+                "output_name": "incorrect_replies",
+                "output_type": List[int],
+            },
+        ]
+    )
+
+    pipe = Pipeline()
+
+    pipe.add_component("prompt_builder", PromptBuilder(template=template))
+    pipe.add_component("generator", FakeGenerator())
+    pipe.add_component("router", router)
+
+    pipe.connect("prompt_builder.prompt", "generator.prompt")
+    pipe.connect("generator.replies", "router.replies")
+    pipe.connect("router.incorrect_replies", "prompt_builder.previous_replies")
+
+    res = pipe.run({"prompt_builder": {"query": "What is the capital of Italy?"}})
+
+    assert res == {"router": {"correct_replies": ["Rome"]}}