diff --git a/config.sub b/config.sub
index 4d248ae..15c57ff 100755
--- a/config.sub
+++ b/config.sub
@@ -885,18 +885,6 @@ case $basic_machine in
 	next | m*-next)
 		cpu=m68k
 		vendor=next
-		case $basic_os in
-		    openstep*)
-		        ;;
-		    nextstep*)
-			;;
-		    ns2*)
-		      basic_os=nextstep2
-			;;
-		    *)
-		      basic_os=nextstep3
-			;;
-		esac
 		;;
 	np1)
 		cpu=np1
@@ -1544,6 +1532,23 @@ case $os in
 	unixware*)
 		os=sysv4.2uw
 		;;
+	# The marketing names for NeXT's operating systems were
+	# NeXTSTEP, NeXTSTEP 2, OpenSTEP 3, OpenSTEP 4.  'openstep' is
+	# mapped to 'openstep3', but 'openstep1' and 'openstep2' are
+	# mapped to 'nextstep' and 'nextstep2', consistent with the
+	# treatment of SunOS/Solaris.
+	ns | ns1 | nextstep | nextstep1 | openstep1)
+		os=nextstep
+		;;
+	ns2 | nextstep2 | openstep2)
+		os=nextstep2
+		;;
+	ns3 | nextstep3 | openstep | openstep3)
+		os=openstep3
+		;;
+	ns4 | nextstep4 | openstep4)
+		os=openstep4
+		;;
 	# es1800 is here to avoid being matched by es* (a different OS)
 	es1800*)
 		os=ose
@@ -1636,9 +1641,6 @@ case $os in
 	nova*)
 		os=rtmk-nova
 		;;
-	ns2)
-		os=nextstep2
-		;;
 	# Preserve the version number of sinix5.
 	sinix5.*)
 		os=`echo "$os" | sed -e 's|sinix|sysv|'`
diff --git a/testsuite/config-sub.data b/testsuite/config-sub.data
index b26d157..915057a 100644
--- a/testsuite/config-sub.data
+++ b/testsuite/config-sub.data
@@ -429,6 +429,19 @@ m68k						m68k-unknown-none
 m68k-bull					m68k-bull-sysv3
 m68k-es1800					m68k-unknown-ose
 m68k-mint					m68k-atari-mint
+m68k-next-nextstep				m68k-next-nextstep
+m68k-next-nextstep1				m68k-next-nextstep
+m68k-next-nextstep2				m68k-next-nextstep2
+m68k-next-nextstep3				m68k-next-openstep3
+m68k-next-nextstep4				m68k-next-openstep4
+m68k-next-ns					m68k-next-nextstep
+m68k-next-ns1					m68k-next-nextstep
+m68k-next-ns2					m68k-next-nextstep2
+m68k-next-ns3					m68k-next-openstep3
+m68k-next-ns4					m68k-next-openstep4
+m68k-next-openstep				m68k-next-openstep3
+m68k-next-openstep1				m68k-next-nextstep
+m68k-next-openstep2				m68k-next-nextstep2
 m68k-next-openstep3				m68k-next-openstep3
 m68k-next-openstep4				m68k-next-openstep4
 m68knommu					m68k-unknown-linux-gnu
@@ -804,6 +817,16 @@ shle-elf					shle-unknown-elf
 simso-wrs					sparclite-wrs-vxworks
 sparc						sparc-sun-sunos4.1.1
 sparc-haiku					sparc-unknown-haiku
+sparc-nextstep					sparc-unknown-nextstep
+sparc-nextstep1					sparc-unknown-nextstep
+sparc-nextstep2					sparc-unknown-nextstep2
+sparc-nextstep3					sparc-unknown-openstep3
+sparc-nextstep4					sparc-unknown-openstep4
+sparc-openstep					sparc-unknown-openstep3
+sparc-openstep1					sparc-unknown-nextstep
+sparc-openstep2					sparc-unknown-nextstep2
+sparc-openstep3					sparc-unknown-openstep3
+sparc-openstep4					sparc-unknown-openstep4
 sparc-solaris					sparc-sun-solaris2
 sparc-solaris1					sparc-sun-sunos4
 sparc-sunos					sparc-sun-sunos