We compute the divisor of Selberg's zeta function for convex cocompact, tor
sion-free discrete groups Gamma acting on a real hyperbolic space of dimens
ion n + 1. The divisor is determined by the eigenvalues and scattering pole
s of the Laplacian on X = Gamma \Hn+1 together with the Euler characteristi
c of X compactified to a manifold with boundary. Ifn is even, the singulari
ties of the zeta function associated to the Euler characteristic of X are i
dentified using work of U. Bunke and M. Olbrich.