diff --git a/shell-completion/bash/systemd-analyze b/shell-completion/bash/systemd-analyze
index f6dc972f031..7a1104c0ad9 100644
--- a/shell-completion/bash/systemd-analyze
+++ b/shell-completion/bash/systemd-analyze
@@ -30,6 +30,11 @@ __get_machines() {
     machinectl list --full --no-legend --no-pager | { while read a b; do echo " $a"; done; };
 }
 
+__get_units_all() {
+    systemctl list-units --no-legend --no-pager --plain --all | \
+        { while read -r a b c; do echo " $a"; done }
+}
+
 __get_services() {
     systemctl list-units --no-legend --no-pager --plain -t service --all $1 | \
         { while read -r a b c; do [[ $b == "loaded" ]]; echo " $a"; done }
@@ -111,6 +116,8 @@ _systemd_analyze() {
     elif __contains_word "$verb" ${VERBS[CRITICAL_CHAIN]}; then
         if [[ $cur = -* ]]; then
             comps='--help --version --system --user --fuzz --no-pager'
+        else
+            comps=$( __get_units_all )
         fi
 
     elif __contains_word "$verb" ${VERBS[DOT]}; then
diff --git a/shell-completion/zsh/_systemd-analyze b/shell-completion/zsh/_systemd-analyze
index 9c33d73f981..2ce8a3a0888 100644
--- a/shell-completion/zsh/_systemd-analyze
+++ b/shell-completion/zsh/_systemd-analyze
@@ -11,6 +11,16 @@
         _files -W '(/run/systemd/ /etc/systemd/ /usr/lib/systemd/)' -P 'systemd/'
     }
 
+(( $+functions[_systemd-analyze_critical-chain] )) ||
+    _systemd-analyze_critical-chain() {
+        local -a _units
+        systemctl list-units --no-legend --no-pager --plain --all |
+        while read -r a b c; do
+            _units+=($a)
+        done
+        compadd -a _units
+    }
+
 (( $+functions[_systemd-analyze_security] )) ||
     _systemd-analyze_security() {
         _sd_unit_files