We present in this paper ultimate boundedness results for a third order nonlinear matrix difierential equations of the form ::: X +A ˜ X + B _ X + H(X) = P(t;X; _ X; ˜ X); where A;B are constant symmetric n £ n matrices, X;H(X) and P(t;X; _ X; ˜ X) are real n£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 difierentiable.