The theory and first implementation of a vibrational coupled cluster (VCC) method for calculations of the vibrational structure of molecules is presented. Different methods for introducing approximate VCC methods are discussed including truncation according to a maximum number of simultaneous mode excitations as well as an interaction space order concept is introduced. The theory is tested on calculation of anharmonic frequencies for a three-mode model system and a formaldehyde quartic force field. The VCC method is compared to vibrational self-consistent-field, vibrational Moller-Plesset perturbation theory, and vibrational configuration interaction (VCI). A VCC calculation typically gives higher accuracy than a corresponding VCI calculation with the same number of parameters and the same formal operation count.(C) 2004 American Institute of Physics.