diff --git a/scrapy/core/spidermw.py b/scrapy/core/spidermw.py
index 5d1ec246c..177d8822a 100644
--- a/scrapy/core/spidermw.py
+++ b/scrapy/core/spidermw.py
@@ -8,6 +8,7 @@ from __future__ import annotations
 
 import logging
 from collections.abc import AsyncIterator, Callable, Coroutine, Iterable
+from contextlib import suppress
 from functools import wraps
 from inspect import isasyncgenfunction, iscoroutine
 from itertools import islice
@@ -108,6 +109,8 @@ class SpiderMiddlewareManager(MiddlewareManager):
             async for r in iterable:
                 yield r
         except Exception as ex:
+            if getattr(ex, "_spidermw_unhandled", False):
+                raise
             exception_result: MutableAsyncChain[_T] = self._process_spider_exception(
                 response, ex, exception_processor_index
             )
@@ -147,6 +150,11 @@ class SpiderMiddlewareManager(MiddlewareManager):
                 f"or an iterable, got {type(result)}"
             )
             raise _InvalidOutput(msg)
+        # Every remaining middleware declined to handle the exception, so the
+        # outer process_spider_output layers must let it through instead of
+        # offering it to those middlewares again.
+        with suppress(AttributeError):
+            exception._spidermw_unhandled = True  # type: ignore[attr-defined]
         raise exception
 
     def _process_spider_output(
diff --git a/tests/test_spidermiddleware_output_chain.py b/tests/test_spidermiddleware_output_chain.py
index dacc90b27..9aa124693 100644
--- a/tests/test_spidermiddleware_output_chain.py
+++ b/tests/test_spidermiddleware_output_chain.py
@@ -243,6 +243,39 @@ class GeneratorOutputChainSpider(Spider):
         yield {"processed": ["parse-second-item"]}
 
 
+# ================================================================================
+# (5) an exception from a spider callback (generator) that no process_spider_exception
+# method handles, with middlewares that define a process_spider_output method
+class FirstUnhandledMiddleware(_GeneratorDoNothingMiddleware):
+    pass
+
+
+class SecondUnhandledMiddleware(_GeneratorDoNothingMiddleware):
+    pass
+
+
+class ThirdUnhandledMiddleware(_GeneratorDoNothingMiddleware):
+    pass
+
+
+class UnhandledExceptionSpider(Spider):
+    name = "UnhandledExceptionSpider"
+    custom_settings = {
+        "SPIDER_MIDDLEWARES": {
+            FirstUnhandledMiddleware: 30,
+            SecondUnhandledMiddleware: 20,
+            ThirdUnhandledMiddleware: 10,
+        },
+    }
+
+    async def start(self):
+        yield Request(self.mockserver.url("/status?n=200"))
+
+    def parse(self, response):
+        yield {"processed": ["parse-first-item"]}
+        raise ImportError
+
+
 # ================================================================================
 class TestSpiderMiddleware:
     mockserver: MockServer
@@ -426,3 +459,20 @@ class TestSpiderMiddleware:
         assert str(item_from_callback) in log4
         assert str(item_recovered) in log4
         assert "parse-second-item" not in log4
+
+    @coroutine_test
+    async def test_unhandled_exception(self, caplog: pytest.LogCaptureFixture) -> None:
+        """
+        (5) An exception that no process_spider_exception method handles should be
+        offered to each of them only once, and then reach the spider error log.
+        """
+        log5 = await self.crawl_log(UnhandledExceptionSpider, caplog)
+        for middleware in (
+            FirstUnhandledMiddleware,
+            SecondUnhandledMiddleware,
+            ThirdUnhandledMiddleware,
+        ):
+            method = f"{middleware.__name__}.process_spider_exception"
+            assert log5.count(f"{method}: ImportError caught") == 1
+        assert "Spider error processing" in log5
+        assert "'item_scraped_count': 1" in log5