We extend a model for layered high-temperature superconductors to systems with two CuO2 layers per unit cell and two interlayer spacings with different physical properties. The carriers are assumed to occupy Fermi liquid states, forming narrow tight-binding bands. The layers are coupled by weak interlayer-hopping matrix elements between adjacent sheets, as well as by an attractive interaction between carriers in neighboring layers in addition to an on-site intralayer coupling. We solve the Gorkov equations for this model to obtain the critical temperature and the density of states of the oneparticle excitations from the superconducting condensate, and discuss various parameter regimes concerning the coupling between the two layers. We compare our results with current experimental findings for high-temperature superconductors. The presence of two CuO2 layers leads to multi-peak features in the superconducting density of states, as has been observed in recent tunneling measurements. © 1990 Springer-Verlag.