The paper is concerned with the study of the uniform ultimate boundedness of solutions of the third-order system of nonlinear delay differential equation \begin{equation*}tackrel{...}{X}+Aḍot{X}+B\dot{X}+H(X(t-r))=P(t,X,\dot{X},ḍot{X}),\end{equation*} where $A, B$ are real $n×n$ constant symmetric matrices, $r$ is a positive real constant and $X\in\R^n,$ using the Lyapunov-Krasovskii functional method and following the arguments used in [1] and [14], we obtained results which give an $n-$dimensional analogue of an earlier result of \cite{17} and extend other earlier results for the case in which we do not necessarily require that $H(X(t-r))$ be differentiable.