ABSTRACT:    The generalized state space of a commutative C*-algebra C(X), denoted S_H (C(X)), is the set of positive unital maps from C(X) to the algebra B(H) of bounded linear operators on a Hilbert space H. C*-convexity is one of several non-commutative analogs of convexity which have been discussed in this context. We will show that a C*-extreme point of S_H (C(X)) satisfies a certain spectral condition on the operators in the range of the associated positive operator-valued measure. If H is finite dimensional, D. Farenick and P. Morenz have shown that every C*-extreme point of S_H (C(X)) is multiplicative. However, their method is fundamentally different from the one used here, which enables us to show that C*-extreme maps from C(X) into K+ are multiplicative. It is then possible determine the structure of these maps.