Based　on　the　works　of　ActorGames　which　introduce　game　semantics　into　actors,　we　remove　the　assumption　of　an　immediate　acknowledgement　to　a　received　message　for　an　actor　in　ActorGames.　This　makes　ActorGames　play　without　alternation　and　a　new　kind　of　game　semantics　called　Non-Alternating　ActorGames　are　introduced.　Through　an　example　of　classical　cluster　computing　called　CCC　and　implemented　by　actors,　we　analyze　the　concurrent　messages　among　actors　and　introduce　the　Non-Alternating　ActorGame　strategy,　composition　of　Non-Alternating　ActorGames,　the　Non-Alternating　ActorGame　category　and　relation　to　concurrent　games.　Both　the　Non-Alternating　ActorGame　strategy,　composition　of　Non-Alternating　ActorGames,　the　Non-Alternating　ActorGame　category　and　relation　to　concurrent　games　have　good　properties.　©　2013　IEEE.