In　this　paper,　the　problem　on　stability　analysis　of　generalized　recurrent　neural　networks　with　a　time-varying　delays　is　considered.　Neither　the　differentiability,　the　monotony　on　these　activation　functions　nor　the　differentiability　on　the　time-varying　delays　are　assumed.　By　employing　a　new　Lyapunov-Krasovskii　function,　a　linear　matrix　inequality　(LMI)　approach　is　developed　to　establish　sufficient　conditions　for　RNNs　to　be　globally　asymptotically　stable.　The　proposed　stability　results　are　less　conservative　than　some　recently　known　ones　in　the　literature.　Finally　an　example　is　given　to　verify　the　effectiveness　of　the　present　criterion.