This paper presents sufficient conditions for the ultimate boundedness of solutions of some system of third-order nonlinear differential equations \begin{equation*}tackrel{...}{X}+\Psi(\dot{X})ḍot{X}+\Phi(X)\dot{X}+H(X)=P(t,X,\dot{X},ḍot{X}),\end{equation*} where $\Psi,\Phi$ are positive definite symmetric matrices, $H, P$ are $n-$vectors continuous in their respective arguments, $X\in\mathbb{R}^n$ and $t\in\mathbb{R}^+=[0,+\infty).$ We do not necessarily require $H(X)$ differentiable to obtain our results. By using the Lyapunov's direct (second) method and constructing a complete Lyapunov function, earlier results are generalized.