diff --git a/man/systemd.unit.xml b/man/systemd.unit.xml
index 9411ea2e03..c618e403f7 100644
--- a/man/systemd.unit.xml
+++ b/man/systemd.unit.xml
@@ -1602,14 +1602,23 @@
           <term><varname>ConditionControlGroupController=</varname></term>
 
           <listitem><para>Check whether given cgroup controllers (e.g. <literal>cpu</literal>) are available
-          for use on the system.</para>
+          for use on the system or whether the legacy v1 cgroup or the modern v2 cgroup hierarchy is used.
+          </para>
 
           <para>Multiple controllers may be passed with a space separating them; in this case the condition
           will only pass if all listed controllers are available for use. Controllers unknown to systemd are
-          ignored. Valid controllers are <literal>cpu</literal>, <literal>cpuset</literal>,
-          <literal>io</literal>, <literal>memory</literal>, and <literal>pids</literal>. Even if available in
-          the kernel, a particular controller may not be available if it was disabled on the kernel command
-          line with <varname>cgroup_disable=controller</varname>.</para></listitem>
+          ignored. Valid controllers are <literal>cpu</literal>, <literal>io</literal>,
+          <literal>memory</literal>, and <literal>pids</literal>. Even if available in the kernel, a
+          particular controller may not be available if it was disabled on the kernel command line with
+          <varname>cgroup_disable=controller</varname>.</para>
+
+          <para>Alternatively, two special strings <literal>v1</literal> and <literal>v2</literal> may be
+          specified (without any controller names). <literal>v2</literal> will pass if the unified v2 cgroup
+          hierarchy is used, and <literal>v1</literal> will pass if the legacy v1 hierarchy or the hybrid
+          hierarchy are used. Note that legacy or hybrid hierarchies have been deprecated. See
+          <citerefentry><refentrytitle>systemd</refentrytitle><manvolnum>1</manvolnum></citerefentry> for
+          more information.</para>
+          </listitem>
         </varlistentry>
 
         <varlistentry>
diff --git a/src/core/unit.c b/src/core/unit.c
index e3a57e3b84..642db41e41 100644
--- a/src/core/unit.c
+++ b/src/core/unit.c
@@ -1546,7 +1546,8 @@ static int unit_add_mount_dependencies(Unit *u) {
 
 static int unit_add_oomd_dependencies(Unit *u) {
         CGroupContext *c;
-        bool wants_oomd;
+        CGroupMask mask;
+        int r;
 
         assert(u);
 
@@ -1557,10 +1558,20 @@ static int unit_add_oomd_dependencies(Unit *u) {
         if (!c)
                 return 0;
 
-        wants_oomd = (c->moom_swap == MANAGED_OOM_KILL || c->moom_mem_pressure == MANAGED_OOM_KILL);
+        bool wants_oomd = c->moom_swap == MANAGED_OOM_KILL || c->moom_mem_pressure == MANAGED_OOM_KILL;
         if (!wants_oomd)
                 return 0;
 
+        if (!cg_all_unified())
+                return 0;
+
+        r = cg_mask_supported(&mask);
+        if (r < 0)
+                return log_debug_errno(r, "Failed to determine supported controllers: %m");
+
+        if (!FLAGS_SET(mask, CGROUP_MASK_MEMORY))
+                return 0;
+
         return unit_add_two_dependencies_by_name(u, UNIT_AFTER, UNIT_WANTS, "systemd-oomd.service", true, UNIT_DEPENDENCY_FILE);
 }