We explore variations of Young measures in order to establish equilibrium conditions for minimizers of generalized variational principles where Young measures enter the minimization problem. The slicing measure decomposition is extremely useful in rendering equilibrium conditions tractable; they usually yield information on the support of generalized minimizers. It also enables us to describe new, equivalent variational principles where these equilibrium constraints are taken into account. The only case where computations can be made explicit is the scalar, one-dimensional case.