We　study　the　dynamic　behaviors　of　a　general　discrete　nonautonomous　system　of　plankton　allelopathy　with　delays.　We　first　show　that　under　some　suitable　assumption,　the　system　is　permanent.　Next,　by　constructing　a　suitable　Lyapunov　functional,　we　obtain　a　set　of　sufficient　conditions　which　guarantee　the　global　attractivity　of　the　two　species.　After　that,　by　constructing　an　extinction-type　Lyapunov　functional,　we　show　that　under　some　suitable　assumptions,　one　species　will　be　driven　to　extinction.　Finally,　two　examples　together　with　their　numerical　simulations　show　the　feasibility　of　the　main　results.