The constraints of unitarity on a multichannel partial-wave amplitude dominated by two nearby or coincident resonances are derived. The factorization conditions are discussed and used in the solution of these equations. The solutions permit variation in the relative heights of the two peaks in the cross section and variation in the depth of the dip. Single peaks appear in some cross sections, while doubled peaks appear in others. The single peak may be centered at the energy of the dip or displaced to either side, and the amplitude may be imaginary or real at the top of the single peak. The doubled-resonance amplitude is Reggeized and the narrow-width limit is investigated. The amplitude becomes a simple pole with an unfactorizable residue in this limit. Numerical examples of the solutions are also presented.