In this paper, we use a modification of Krasnoselskii's fixed point theorem introduced by Burton (see b0 Theorem 3) to obtain stability results of the zero solution of the totally nonlinear neutral differential equations with functional delayx′(t)=-a(t)h(x(t-τ(t)))+c(t)x′(t-τ(t))+G(t,x(t),x(t-τ(t))).The stability of the zero solution of this eqution provided that h(0)=G(t,0,0)=0. The Caratheodory condition is used for the function G
