Certain　classes　of　systems　with　nonlinearities　of　a　sector　type　and　time-varying　delay　are　studied.　By　the　use　of　the　Lyapunov　functions　method　and　the　Razumikhin　approach,　conditions　are　obtained　under　which　the　zero　solution　of　considered　systems　is　asymptotically　stable　for　an　arbitrary　continuous　nonnegative　and　bounded　delay.　Moreover,　estimates　of　the　convergence　rate　of　solutions　are　derived.