diff --git a/spec/ruby/core/process/clock_gettime_spec.rb b/spec/ruby/core/process/clock_gettime_spec.rb
index 70ec2c4bb5..a7b6bd2b02 100644
--- a/spec/ruby/core/process/clock_gettime_spec.rb
+++ b/spec/ruby/core/process/clock_gettime_spec.rb
@@ -1,11 +1,14 @@
 require_relative '../../spec_helper'
 
 describe "Process.clock_gettime" do
-  # This does not succeed with some platforms:
-  # RHEL: https://rubyci.org/logs/rubyci.s3.amazonaws.com/rhel_zlinux/ruby-trunk/log/20181229T063303Z.fail.html.gz
-  # Solaris: https://rubyci.org/logs/rubyci.s3.amazonaws.com/unstable11x/ruby-trunk/log/20181229T002409Z.fail.html.gz
   platform_is_not :windows, :solaris do
-    Process.constants.select { |c| c.to_s.start_with?('CLOCK_') }.each do |c|
+    Process.constants.select { |c|
+      c.to_s.start_with?('CLOCK_') &&
+      # These require CAP_WAKE_ALARM and are not documented in clock_gettime(),
+      # they return EINVAL if the permission is not granted.
+      c != :CLOCK_BOOTTIME_ALARM &&
+      c != :CLOCK_REALTIME_ALARM
+    }.each do |c|
       it "can be called with Process::#{c}" do
         value = Process.const_get(c)
         Process.clock_gettime(value).should be_an_instance_of(Float)