A problem of control of a mechanical system in a partly specified motion is studied. It is shown that the structure of differential-algebraic equations (DAEs) describing the problem may essentially differ from the structure of governing equations for a constrained mechanical system. The control forces chosen to realize the program constraints may have arbitrary directions with respect to the constraint manifold, and, in the extreme, they may be tangent. Thus, the index of the original DAEs of the problem may exceed three and a special approach to the problem solution has to be undertaken. Such an approach is proposed; a systematic formulation is given for the transformation of the DAEs into index-one DAEs or ODEs. Criteria for solvability of the problem are included.