The resonance structure in the cross section for rotational excitation of H2 by Li+ in a small energy range above the j = 2 threshold has been examined. The usual close-coupling formalism has been employed with the Lester hypersurface. The observed resonances are believed to be shape resonances strongly perturbed by the anisotropic potential, which makes characterization of the resonances extremely difficult. The use of the eigenphases has been helpful in the study of these resonances. Copyright © 1976 American Institute of Physics.