We present in this paper ultimate boundedness results for a third order nonlinear matrix differential equations of the form $$t{...}{X}+Aḍot{X}+B\dot{X}+H(X)=P(t,X,\dot{X},ḍot{X}),$$ where $A, B$ are constant symmetric $n\times n$ matrices, $X, H(X)$ and $P(t,X,\dot{X},\ddot{X})$ are real $n\times n$ matrices continuous in their respective arguments. Our results give a matrix analogue of earlier results of Afuwape [1] and Meng [4], and extend other earlier results for the case in which we do not necessarily require that $H(X)$ be differentiable.