The method of moments of coupled-cluster equations (MMCC) and the renormalized coupled-cluster (CC) approaches [see, e.g., K. Kowalski and P. Piecuch, J. Chem. Phys. 113, 18 (2000)] are extended to potential energy surfaces involving multiple bond breaking by introducing the new quasivariational (QV) and quadratic (Q) MMCC approximations. The QMMCC approximations retain the single-reference and noniterative character of the renormalized CC methods, while allowing us to obtain the highly accurate description of multiple bond stretching or breaking. The discussion of the general QVMMCC and QMMCC theories is augmented by the results of test calculations for the double dissociation of H2O and triple bond breaking in N-2. (C) 2003 American Institute of Physics.