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)　-　Sigma(j=1)(m)　b(j)(t)u(t　-　tau(j)(t,u(t)))/k(t)　+　c(t)u(t)　+　Sigma(j=1)(m)　d(j)(t)u(t　-　eta(j)(t,u(t)))},　where　r(t),　k(t),　a(t),　b(j)(t),　d(j)(t),　j　=　1,2,...,m,　are　continuous,　real-valued　periodic　functions　with　period　omega　＞　0　and　r(t),　k(t),　a　(t)　＞　0;　b(j)(t),　d(j)　(t)　greater　than　or　equal　to　0,　j　=　1,　2,...,　m,　are　periodic　continuous　functions　with　period　omega　＞　0,　tau(j),　eta(j)　are　omega-periodic　with　respect　to　their　first　arguments.　Some　new　results　are　obtained.　(C)　2003　Elsevier　Inc.　All　rights　reserved.