diff --git a/scripts/package/builddeb b/scripts/package/builddeb
index e8ca6dc97e96..c4c580f547ef 100755
--- a/scripts/package/builddeb
+++ b/scripts/package/builddeb
@@ -132,6 +132,11 @@ fi
 if [ "$ARCH" != "um" ]; then
 	$MAKE -f $srctree/Makefile headers
 	$MAKE -f $srctree/Makefile headers_install INSTALL_HDR_PATH="$libc_headers_dir/usr"
+	# move asm headers to /usr/include/<libc-machine>/asm to match the structure
+	# used by Debian-based distros (to support multi-arch)
+	host_arch=$(dpkg-architecture -a$(cat debian/arch) -qDEB_HOST_MULTIARCH)
+	mkdir $libc_headers_dir/usr/include/$host_arch
+	mv $libc_headers_dir/usr/include/asm $libc_headers_dir/usr/include/$host_arch/
 fi
 
 # Install the maintainer scripts
diff --git a/scripts/package/mkdebian b/scripts/package/mkdebian
index 8351584cb24e..e0750b70453f 100755
--- a/scripts/package/mkdebian
+++ b/scripts/package/mkdebian
@@ -197,6 +197,7 @@ Architecture: $debarch
 Description: Linux support headers for userspace development
  This package provides userspaces headers from the Linux kernel.  These headers
  are used by the installed headers for GNU glibc and other system libraries.
+Multi-Arch: same
 
 Package: $dbg_packagename
 Section: debug