A　nonlinear　differential　equation　system　with　nonlinearities　of　a　sector　type　is　studied.　Using　the　Lyapunov　direct　method　and　the　comparison　method,　conditions　are　derived　under　which　the　zero　solution　of　the　system　is　stable　with　respect　to　all　variables　and　asymptotically　stable　with　respect　to　a　part　of　variables.　Moreover,　the　impact　of　nonstationary　perturbations　with　zero　mean　values　on　the　stability　of　the　zero　solution　is　investigated.　In　addition,　the　corresponding　time-delay　system　is　considered　for　which　delay-independent　partial　asymptotic　stability　conditions　are　found.　Three　examples　are　presented　to　demonstrate　effectiveness　of　the　obtained　results.