A　scheme　is　presented　for　realizing　quantum　logic　gates　for　two　atoms　localized　in　two　distant　optical　cavities.　Our　scheme　works　in　a　regime　in　which　the　atom-cavity　coupling　strength　is　smaller　than　the　cavity　decay　rate.　Thus　the　requirement　on　the　quality　factor　of　the　cavities　is　greatly　relaxed.　Further　more,　the　fidelity　of　our　scheme　is　not　affected　by　detection　inefficiency　and　atomic　decay.　These　advantages　are　important　in　view　of　experiment.