A new effective Hamiltonian is presented for the analysis of the high-resolution spectra of open-shell van der Waals complexes containing the O-2 molecule. The effects of electron spin are included but the complications of nuclear spin and resultant nuclear spin splitting are neglected. The Hamiltonian is composed of the rotational, centrifugal distortion, and spin-spin interaction terms. The resulting energy levels are divided into two well-separated groups and the pattern is a complicated function of theta (the angle that the O-2 molecule makes with the principal a axis of the complex) and phi (the azimuthal angle of the O-2 out of the plane defined by the a and b axes of the complex). This model has been successfully applied to analyze the high-resolution spectrum of O-2-N2O in the region of the N2O monomer nu(3) vibrational band, which will be presented in a separate paper. (C) 1997 American Institute of Physics.