diff --git a/Lib/test/test_socket.py b/Lib/test/test_socket.py
index 6e9394b19aa6fda..14865bac0646e62 100644
--- a/Lib/test/test_socket.py
+++ b/Lib/test/test_socket.py
@@ -57,6 +57,9 @@
 # SCM_RIGHTS control message when several are sent in a single sendmsg().
 BSD_COMBINES_SCM_RIGHTS = sys.platform.startswith(
     ("netbsd", "openbsd", "dragonfly"))
+# OpenBSD and DragonFly fail recvmsg() with EMSGSIZE, instead of setting
+# MSG_CTRUNC, when the ancillary data buffer is too small for a cmsghdr.
+CMSG_TRUNC_RAISES_EMSGSIZE = sys.platform.startswith(("openbsd", "dragonfly"))
 WSL = "microsoft-standard-WSL" in platform.release()
 
 try:
@@ -4145,6 +4148,7 @@ def _testCmsgTrunc0(self):
     # (but still too small) buffer sizes.
 
     @skipForRefleakHuntinIf(sys.platform == "darwin", "#80931")
+    @unittest.skipIf(CMSG_TRUNC_RAISES_EMSGSIZE, "skipping, see gh-154240")
     def testCmsgTrunc1(self):
         self.checkTruncatedHeader(self.doRecvmsg(self.serv_sock, len(MSG), 1))
 
@@ -4153,6 +4157,7 @@ def _testCmsgTrunc1(self):
         self.createAndSendFDs(1)
 
     @skipForRefleakHuntinIf(sys.platform == "darwin", "#80931")
+    @unittest.skipIf(CMSG_TRUNC_RAISES_EMSGSIZE, "skipping, see gh-154240")
     def testCmsgTrunc2Int(self):
         # The cmsghdr structure has at least three members, two of
         # which are ints, so we still shouldn't see any ancillary
@@ -4165,6 +4170,7 @@ def _testCmsgTrunc2Int(self):
         self.createAndSendFDs(1)
 
     @skipForRefleakHuntinIf(sys.platform == "darwin", "#80931")
+    @unittest.skipIf(CMSG_TRUNC_RAISES_EMSGSIZE, "skipping, see gh-154240")
     def testCmsgTruncLen0Minus1(self):
         self.checkTruncatedHeader(self.doRecvmsg(self.serv_sock, len(MSG),
                                                  socket.CMSG_LEN(0) - 1))
@@ -4202,6 +4208,7 @@ def checkTruncatedArray(self, ancbuf, maxdata, mindata=0):
         self.checkFDs(fds)
 
     @skipForRefleakHuntinIf(sys.platform == "darwin", "#80931")
+    @unittest.skipIf(CMSG_TRUNC_RAISES_EMSGSIZE, "skipping, see gh-154240")
     def testCmsgTruncLen0(self):
         self.checkTruncatedArray(ancbuf=socket.CMSG_LEN(0), maxdata=0)
 
@@ -4210,6 +4217,7 @@ def _testCmsgTruncLen0(self):
         self.createAndSendFDs(1)
 
     @skipForRefleakHuntinIf(sys.platform == "darwin", "#80931")
+    @unittest.skipIf(CMSG_TRUNC_RAISES_EMSGSIZE, "skipping, see gh-154240")
     def testCmsgTruncLen0Plus1(self):
         self.checkTruncatedArray(ancbuf=socket.CMSG_LEN(0) + 1, maxdata=1)
 
@@ -4218,6 +4226,7 @@ def _testCmsgTruncLen0Plus1(self):
         self.createAndSendFDs(2)
 
     @skipForRefleakHuntinIf(sys.platform == "darwin", "#80931")
+    @unittest.skipIf(CMSG_TRUNC_RAISES_EMSGSIZE, "skipping, see gh-154240")
     def testCmsgTruncLen1(self):
         self.checkTruncatedArray(ancbuf=socket.CMSG_LEN(SIZEOF_INT),
                                  maxdata=SIZEOF_INT)
@@ -4228,6 +4237,7 @@ def _testCmsgTruncLen1(self):
 
 
     @skipForRefleakHuntinIf(sys.platform == "darwin", "#80931")
+    @unittest.skipIf(CMSG_TRUNC_RAISES_EMSGSIZE, "skipping, see gh-154240")
     def testCmsgTruncLen2Minus1(self):
         self.checkTruncatedArray(ancbuf=socket.CMSG_LEN(2 * SIZEOF_INT) - 1,
                                  maxdata=(2 * SIZEOF_INT) - 1)
@@ -4500,6 +4510,7 @@ def _testSingleCmsgTrunc0(self):
     # (but still too small) buffer sizes.
 
     @requireAttrs(socket, "IPV6_RECVHOPLIMIT", "IPV6_HOPLIMIT")
+    @unittest.skipIf(CMSG_TRUNC_RAISES_EMSGSIZE, "skipping, see gh-154240")
     def testSingleCmsgTrunc1(self):
         self.checkHopLimitTruncatedHeader(ancbufsize=1)
 
@@ -4509,6 +4520,7 @@ def _testSingleCmsgTrunc1(self):
         self.sendToServer(MSG)
 
     @requireAttrs(socket, "IPV6_RECVHOPLIMIT", "IPV6_HOPLIMIT")
+    @unittest.skipIf(CMSG_TRUNC_RAISES_EMSGSIZE, "skipping, see gh-154240")
     def testSingleCmsgTrunc2Int(self):
         self.checkHopLimitTruncatedHeader(ancbufsize=2 * SIZEOF_INT)
 
@@ -4518,6 +4530,7 @@ def _testSingleCmsgTrunc2Int(self):
         self.sendToServer(MSG)
 
     @requireAttrs(socket, "IPV6_RECVHOPLIMIT", "IPV6_HOPLIMIT")
+    @unittest.skipIf(CMSG_TRUNC_RAISES_EMSGSIZE, "skipping, see gh-154240")
     def testSingleCmsgTruncLen0Minus1(self):
         self.checkHopLimitTruncatedHeader(ancbufsize=socket.CMSG_LEN(0) - 1)
 
@@ -4527,6 +4540,7 @@ def _testSingleCmsgTruncLen0Minus1(self):
         self.sendToServer(MSG)
 
     @requireAttrs(socket, "IPV6_RECVHOPLIMIT", "IPV6_HOPLIMIT")
+    @unittest.skipIf(CMSG_TRUNC_RAISES_EMSGSIZE, "skipping, see gh-154240")
     def testSingleCmsgTruncInData(self):
         # Test truncation of a control message inside its associated
         # data.  The message may be returned with its data truncated,
@@ -4599,6 +4613,7 @@ def _testSecondCmsgTrunc0(self):
 
     @requireAttrs(socket, "CMSG_SPACE", "IPV6_RECVHOPLIMIT", "IPV6_HOPLIMIT",
                   "IPV6_RECVTCLASS", "IPV6_TCLASS")
+    @unittest.skipIf(CMSG_TRUNC_RAISES_EMSGSIZE, "skipping, see gh-154240")
     def testSecondCmsgTrunc1(self):
         self.checkTruncatedSecondHeader(socket.CMSG_SPACE(SIZEOF_INT) + 1)
 
@@ -4609,6 +4624,7 @@ def _testSecondCmsgTrunc1(self):
 
     @requireAttrs(socket, "CMSG_SPACE", "IPV6_RECVHOPLIMIT", "IPV6_HOPLIMIT",
                   "IPV6_RECVTCLASS", "IPV6_TCLASS")
+    @unittest.skipIf(CMSG_TRUNC_RAISES_EMSGSIZE, "skipping, see gh-154240")
     def testSecondCmsgTrunc2Int(self):
         self.checkTruncatedSecondHeader(socket.CMSG_SPACE(SIZEOF_INT) +
                                         2 * SIZEOF_INT)
@@ -4620,6 +4636,7 @@ def _testSecondCmsgTrunc2Int(self):
 
     @requireAttrs(socket, "CMSG_SPACE", "IPV6_RECVHOPLIMIT", "IPV6_HOPLIMIT",
                   "IPV6_RECVTCLASS", "IPV6_TCLASS")
+    @unittest.skipIf(CMSG_TRUNC_RAISES_EMSGSIZE, "skipping, see gh-154240")
     def testSecondCmsgTruncLen0Minus1(self):
         self.checkTruncatedSecondHeader(socket.CMSG_SPACE(SIZEOF_INT) +
                                         socket.CMSG_LEN(0) - 1)
@@ -4631,6 +4648,7 @@ def _testSecondCmsgTruncLen0Minus1(self):
 
     @requireAttrs(socket, "CMSG_SPACE", "IPV6_RECVHOPLIMIT", "IPV6_HOPLIMIT",
                   "IPV6_RECVTCLASS", "IPV6_TCLASS")
+    @unittest.skipIf(CMSG_TRUNC_RAISES_EMSGSIZE, "skipping, see gh-154240")
     def testSecondCmsgTruncInData(self):
         # Test truncation of the second of two control messages inside
         # its associated data.