Abstract : This report summarizes a body of research dealing with the nonlinear control theory of complex mechanical systems. The principal focus is on so-called superarticulated (or underactuated) mechanical systems and systems having a mixture of directly controlled as well as uncontrolled degrees of freedom. The two-fold goal of the research is: (1) how to control the degrees of freedom which are directly actuated without eliciting undesired behavior in the unactuated degrees of freedom, and (2) how to prescribe motions of the directly actuated degrees of freedom which are not directly controlled. The report contains a comprehensive list of research published under this grant as well as some predecessor grants. Two papers in particular 'The Geometry of Controlled Mechanical Systems' and 'Open loop Oscillatory Stabilization of an n-Pendulum' comprise the present report.