A global reduction theory of the vibration–rotational Hamiltonian of C3v closed-shell molecules, dealing with all possible anharmonic interactions in which a fundamental vibration can be involved, is presented. The effective correlation-free Hamiltonians and the corresponding matrix elements are derived. The cases studied here are (i) a fundamental band interacting with an overtone, (ii) a fundamental band interacting with a combination band. The Hamiltonian terms H30;H31;H32 and the recommended set of parameters following from the appropriate reductions are presented. The results are provided in a form directly applicable to the analysis of spectra of the interacting states.