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)　-　beta(t)n(t)　-　Sigmai=1nbi(t)n(t　-　taui(t))　-　Sigmai=1nci(t)n＇(t　-　gammai(t))　-　delta(t)u(t)　-　Sigmai=1ndi(t)u(t　-　sigmai(t))],)(du/dt　=　-e(t)u(t)　+　f(t)n(t)　+　Sigmai=1ngi(t)n(t　-　etai(t)).)　Our　results　extend　and　improve　existing　results,　and　have　further　applications　in　population　dynamics.　(C)　2003　Elsevier　Inc.　All　rights　reserved.