The two-exciton wave functions of conjugated dendrimers with fractal geometries are calculated using the Frenkel-exciton model. Self-similarity and the high degree of symmetry make it possible to express the two-photon spectra of these chromophore aggregates in a compact form using irreducible representations of optical excitations, single-exciton states, and an effective two-exciton transition dipole moment. The explicit calculation of the complete manifold of two-exciton states which involves an expensive l(3)xl(3) diagonalization, l being number of generations, is totally avoided. A real space analysis shows that the two-exciton states and resonances are dominated by periphery chromophores due to their exponentially large number.