Using a linear-response approach, the recently introduced spin-restricted coupled-cluster (SR-CC) theory is extended to the treatment of excited states of high-spin open-shell molecules. Explicit equations are given within the usual singles and doubles approximation and our implementation (within an existing spin-orbital code) is described. It is shown that in SR-CC theory, due to spin constraints, the spin-expectation value for the excited states calculated as corresponding energy derivatives always corresponds to the exact value. In addition, the SR-CC singles and doubles (SR-CCSD) approach is extended to include also the so-called pseudotriple excitations (best described as double excitations with an additional spin-flip in one open-shell orbital) which are important for the description of so-called low-spin excited states. Exploratory calculations for a few diatomic systems (BeH, OH, NO, CN, and CO+) show that problems due to spin contamination in the unrestricted Hartree-Fock (UHF) CCSD treatment of excited states are rectified by using a restricted open-shell Hartree-Fock (ROHF) reference, as it is done in the SR-CC approach. While SR-CCSD performs well for high-spin excited states, the closely related partially spin-adapted (PSA) CC approach is shown to be inferior and errors in the computed excitation energies are generally larger than the typical accuracy of about 0.2 eV in CCSD excited state treatments. So-called low-spin states (e.g., the 2 B-2(1) state of NH2) are shown to require inclusion of pseudotriple excitations for even a qualitatively correct description. If they are included, ROHF-CC, SR-CC, and PSA-CC give essentially identical results. (C) 2000 American Institute of Physics. [S0021- 9606(00)31208-9].