Abstract
In this paper, we use a modification of Krasnoselskii's fixed point theorem introduced by Burton and the Caratheodory condition to obtain stability results of the zero solution of the neutral nonlinear differential equations with variable delay x' (t) = -a(t)h(x(t)) + c(t)x'(t -tau(t)) + G (t, x(t),x(t - tau(t))). The stability of the zero solution of this eqution provided that h (0) = G (t, 0, 0) = 0.