We analyze the structure of models with unbroken and spontaneously broken U(1) a × U(1) b gauge symmetry. We show that the quantum corrections to the 2 N gauge charges, with N = number of fermions + number of scalars, can be absorbed in the redefinition of three independent gauge couplings ( ga, gb, and gab). We establish the (one-loop) conditions on the matter content for gab = 0 (a value usually assumed in the literature) and we show that in the minimal extensions of the Standard Model with an extra U(1) symmetry the choice gab = 0 is not stable under radiative corrections induced by the standard Higgs fields. Moreover, gab = 0 to all orders seems to require an exact symmetry. The spontaneous breaking of the gauge symmetry induces further mixing between the two gauge bosons and introduces a fourth independent physical parameter. A consequence of our analysis is that the usual tree-level description with only three physical parameters (i.e., two gauge couplings and one gauge boson mixing angle) is not in general a justified zero order limit of the treatment including radiative corrections.