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　nonlinear　state　dependent　delays　predator-prey　system　equation　presented　where　a　i　(t),　c　j　(t),　d　i　(t)　are　continuous　positive　periodic　functions　with　periodic　ω　>　0,　b　1(t),　b　2(t)　are　continuous　periodic　functions　with　periodic　ω　and　equation　presented　are　positive　constants.　©　2005　Springer-Verlag　Berlin　Heidelberg.