© 2022 Watam Press.In this work, we address a third order differential equation with generalized pieewise onstant argument. Investigation onerning the existene, uniqueness of the solutions of the equation is performed. Suffiient onditions that guarantee the existene of uniformly asymptotially stable trivial solution are given on the basis of both Lyapunov-Krasovskii and Lyapunov-Razumikhin methods. The results are supported by an example and a simulation.