[en] Integral equations for construction of a crossing-symmetric unitary Regge theory are extended to allow two coupled two-body channels. As in the case of a single channel, spectral functions are represented as Watson-Sommerfeld integrals over continued partial waves. A new type of partial wave is needed to represent one of the spectral functions in a region where one channel is open and the other is closed. This leads to certain difficulties in allowing realistic Regge poles