Abstract: A delay differential inequality,which is of impartance to the research for the stability of delay system,was established in Ref. by A.Halanay.However,as far as the stability of Neutral system is concerned,Halanay's inequality is hard to apply.This paper generalizes the delay differential inequality and establishes a delay integral inequality.Applying this inequality to study the neutral differential equations,some simple sufficient criteria are obtained for judging global exponential stability.