Electronic Journal of Differential Equations, Vol. 2006(2006), No. 117, pp. 1-11. Title: Existence and uniqueness of periodic solutions for first-order neutral functional differential equations with two deviating arguments Authors: Jinsong Xiao (Hunan City Univ., China) Bingwen Liu (Jiaxing Univ., China) Abstract: In this paper, we use the coincidence degree theory to establish the existence and uniqueness of T-periodic solutions for the first-order neutral functional differential equation, with two deviating arguments, $$ (x(t)+Bx(t-\delta))'= g_{1}(t,x(t-\tau_{1}(t))) +g_{2}(t,x(t-\tau_{2}(t))) +p(t). $$ Submitted March 16, 2006. Published September 26, 2006. Math Subject Classifications: 34C25, 34D40. Key Words: First order; neutral; functional differential equations; deviating argument; periodic solutions; coincidence degree.