Abstract: In this paper, the authors study a kind of nonlinear thirdorder delay differential equations as follows,x+g(x,x)x+f(x(t-T2(t)))=p(t,x,x,x))By using the second method of Lyapunov, the researchers establish some sufficient conditions for the global asymptotic stability of the zero solution and the boundedness of all solutions to it.

Key words: delay differential equations; global asymptotic stability; boundedness; Lyapunov functional