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　neutral　model　with　periodic　delays　and　feedback　control　{dn/dt=n(t)[a(t)-β(t)n(t)-∑i=1　nbi(t)n(t-τi(t))-∑i=1　nci(t)n′(t-γi(t))-δ(t)u(t)　-∑i=1ndi(t)u(t-σi(t))],du/　dt=-e(t)u(t)+f(t)n(t)+∑i=1ngi(t)n(t-　ηi(t)).　Our　results　extend　and　improve　existing　results,　and　have　further　applications　in　population　dynamics.　©　2003　Elsevier　Inc.　All　rights　reserved.