This paper presents an operational space control approach for the general class of holonomically constrained multibody systems. As a point of departure, the general formulation of constrained dynamical systems is addressed using multiplier and minimization approaches. The constrained dynamics problem is interpreted with respect to its underlying symmetry with task space dynamics. A framework for constrained operational space control is then presented which casts the general formulation of constrained multibody systems into a task space setting. This provides a means of exploiting natural task-level control structures within the constrained environment. A set of examples illustrate this control implementation.