Mechanical manipulators belong to the class of non-linear multivariable systems. Their dynamics are a complex and highly non-linear function of the system configurations and loads. In this paper, model-following control laws based on the 'second method' of Lyapunov are developed for the dynamic control of a manipulator. These control laws are derived from the dynamic model of the manipulator and force the manipulator to track a linear second-order non-interacting model whose dynamic characteristics are chosen by the designer. The control systems resulting from these control laws were compared and tested on a simulated manipulator. Simulation results demonstrate the effectiveness of this approach. A method is also developed to estimate the mass of the external loads if these are not known. This method enables the controllers to properly compensate for the effect of the loads on the manipulator.