Adaptive robust control (ARC) of MIMO nonlinear systems transformable to two semi-strict feedback forms are considered. The forms can have both parametric uncertainties and uncertain nonlinearities such as external disturbances. In addition, the forms allow coupling and appearance of parametric uncertainties in the input matrix of each layer. Furthermore, the usual assumption on the linear parametrization of the state equations is relaxed to the extent that the forms are applicable to the control of some mechanical systems. To deal with the complexity and difficulties caused by the coupling and the appearance of parametric uncertainties in the input matrices, an ARC Lyapunov function-an extension of the adaptive control Lyapunov function (aclf)-is used to formalize the viewpoint and the achievable results of the recently proposed ARC approach. Two backstepping designs via ARC Lyapunov functions are presented. The results are then used to construct specific ARC control laws for MIMO nonlinear systems in the semi-strict-feedback forms. By using trajectory initialization, the resulting ARC law achieves a guaranteed output tracking transient performance and final tracking accuracy in general. while keeping all physical states and control inputs bounded. In addition, the control law achieves asymptotic output tracking in the presence of parametric uncertainties without using a discontinuous or infinite-gain feedback term.