Abstract: This paper considers the following boundary value problems for functional differential equations: x' (t) = f(t, x_t) (0<t<b) ,x₀ = x_1, and x"(t) = f(t,x_t, x' (t)) (0<t<b) ,  x(b) = B. By using certain fixed point theorem based on degree theory,some sufficient conditions for solvability of the above problems are given.

Key words: functional differential equation, boundary value problem, fixed point theorem ,