We extend the vibrational self-consistent field method (VSCF), and two types of state mixing [denoted VSCF-CI and V-CI (configuration interaction)]: to include an approximate, adiabatic treatment of overall rotation. In this approach, the asymmetric-top rotational Hamiltonian is diagonalized in an "instantaneous" principal axis system, and the resulting coordinate-dependent rotational energy is added to the exact Hamiltonian of the nonrotating system to form an effective Hamiltonian for the rotation/vibrational energies. The energy eigenvalues of that Hamiltonian are then obtained by the VSCF approach and/or variational, stare-mixing methods. In this present formulation for many-mode systems, we use the general Watson Hamiltonian, and also a hierarchical representation of the many-mode potential described previously [S. Carter, S. Culik, and J. M. Bowman, J. Chem. Phys. 107, 10458 (1997)]. This approach, at the VSCF, and VSCF-CI and V-CI levels is tested against recent exact calculations of vibrational/rotation energies of HO2 and H2O. HO2 is an approximate prolate symmetric top, which is a favorable case for the approximate treatment of rotation, whereas H2O is a highly asymmetric top with large rotation constants, and represents an unfavorable case for the method.