We consider a Palatini variation on a generalized Einstein-Hilbert action. We find that the Hilbert constraint, that the connection equals the Christoffel symbol, arises only as a special case of this general action, while for particular values of the coefficients of this generalized action, the connection is completely unconstrained. We discuss the relationship between this situation and that usually encountered in the Palatini formulation.

We consider a Palatini variation on a general N -Dimensional second order, torsionfree dilaton gravity action and determine the resulting equations of motion. Consistency is checked by considering the restraint imposed due to invariance of the matter action under simple coordinate transformations, and the special case of N = 2 is examined. We also examine a sub-class of theories whereby a Palatini variation dynamically coincides with that of the "ordinary" Hilbert variational principle; in particular we examine a generalized Brans-Dicke theory and the associated role of conformal transformations.

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