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　a　food-limited　population　model　with　toxicant　and　state　dependent　delays,　that　is　du(t)/dt　=　u(t)　{r(t)　-　a(t)u(t)　-　∑j=1　m　bj(t)u(t　-　τj(t,　u(t)))/k(t)　+　c(t)u(t)　+　∑j=1　m　dj(t)u(t　-　ηj(t,　u(t)))},　where　r(t),　k(t),　a(t),　bj(t),　dj(t),　j　=　1,　2,...,　m,　are　continuous,　real-valued　periodic　functions　with　period　ω　>　0　and　r(t),　k(t),　a(t)　>　0;　bj(t),　dj(t)　≥　0,　j　=　1,　2,...,　m,　are　periodic　continuous　functions　with　period　ω　>　0,　τj,　ηj　are　ω-periodic　with　respect　to　their　first　arguments.　Some　new　results　are　obtained.　©　2003　Elsevier　Inc.　All　rights　reserved.