The recently proposed method of moments of coupled-cluster equations (MMCC) is extended to excited states via the equation-of-motion coupled-cluster (EOMCC) formalism. The main idea of the new MMCC theory is that of the noniterative energy corrections which, when added to the excited-state energies obtained in standard approximate EOMCC calculations, recover the exact energies. The MMCC corrections are expressed in terms of the generalized moments of the EOMCC equations. Approximate variants of the excited-state MMCC formalism, including the MMCC(2,3) approach, are introduced. In the MMCC(2,3) method, very simple energy corrections, expressed in terms of matrix elements of the triples-reference, triples-singles, and triples-doubles blocks of the EOMCCSD (EOMCC singles and doubles) similarity-transformed Hamiltonian, are added to the excited-state energies obtained in EOMCCSD calculations. The performance of the MMCC(2,3) approach is illustrated by the results of pilot calculations for the potential energy curves of ground and excited states of CH+.