An extension of a model-based tracking control strategy to underactuated systems is presented. Originally, it is designed for actuated systems that can perform tasks specified by equations of algebraic or differential constraints referred to as programmed, which may be nonintegrable. It is demonstrated that for both actuated and underactuated nonholonomically constrained systems one tracking control strategy can be designed. Systems we consider are nonholonomic because of constraints put on their motions as well as unactuated degrees of freedom. We detail an example, which illustrates the theory and demonstrates advantages of application of one tracking control strategy for actuated and underactuated constrained systems.