A model of a local orbital coupled through repulsive interactions to both the hybridizing and the screening channels of a conduction band is solved by Wilson's renormalization group method. At particle-hole symmetry we find non-Fermi-liquid lines of critical points when the interaction in the screening channel is above a critical value. Away from particle-hole symmetry the system displays two stable Fermi-liquid fixed points of different symmetries, separated by a non-Fermi liquid quantum critical point, in the mixed-valence regime. The behavior in the vicinity of this point is consistent with the marginal Fermi-liquid hypothesis. © 1993 The American Physical Society.