Abstract <p> The Regge–Gribov model describing interacting pomerons and odderons is proposed with triple reggeon vertices taking into account the negative signature of the odderon. Its simplified version with zero transverse dimensions is first considered. No phase transition occurs in this case at the intercept crossing unity. This simplified model is studied without further approximations by numerical techniques. The physically relevant model in the two-dimensional transverse space is then studied by the renormalization group method in the single-loop approximation. The pomeron and odderon are taken to have different bare intercepts and slopes. The behavior when the intercepts move from below to their critical values compatible with the Froissart bound is studied. Five real fixed points are found with singularities in the form of nontrivial branch points indicating a phase transition as the intercepts cross unity. The new phases, however, are not physical, since they violate projectile–target symmetry. In the vicinity of fixed points, the asymptotic behavior of Green’s functions and the elastic scattering amplitude is found under the Glauber approximation for couplings to participants. </p>