The effect of strong electron-electron interactions (described by the single-band Hubbard Hamiltonian) on the electronic spectrum and cohesive energies of substitutionally disordered alloys has been studied. The authors use the Hubbard III solution to treat the correlations and coherent-potential approximation for configurational averaging. The use of the Lorentzian form of the host metal density of states enables them to obtain analytical expressions for various quantities of interest. Questions related to the problem of the calculations of cohesive energies in disordered systems with correlations are discussed and partially resolved.