With　the　help　of　a　continuation　theorem　based　on　Gaines　and　Mawhin＇s　coincidence　degree,　easily　verifiable　criteria　are　established　for　the　global　existence　of　positive　periodic　solutions　of　the　following　several　delays　logistic　type　system:　du(t)/dt=u(t)　left　ceiling　a(t)　-　∑bj(t)　(u(t　-　τj(t)))θjright　ceiling,　where　a(t),　bj(t)　are　positive　periodic　continuous　functions　with　periodic　ω　>　0,　Tj(t)　are　nonnegative　continuous　periodic　functions　with　periodic　ω　>　0.　After　that,　by　constructing　a　suitable　Lyapunov　functional,　some　sufficient　conditions　which　guarantee　the　stability　of　the　positive　periodic　solutions　are　obtained.　©2004　Elsevier　Ltd.　All　rights　reserved.