High order perturbative computations for the lowest lying singlet states of the CH2 molecule are used to analyze the efficacy of various multireference perturbation methods (MRPTs). Whereas traditional Moller-Plesset MRPT calculations produce divergent perturbation expansions, the effective Hamiltonian H-upsilon and intermediate Hamiltonian H-int approaches produce well behaved expansions for well-chosen reference spaces. The three methods are compared to assess their convergence properties, the sources of divergence when appropriate, their accuracy when truncated at low orders, and their behavior when applied in conjunction with large reference spaces. The analysis of the sources of divergent or slowly convergent perturbation expansions provides insights into necessary ingredients for useful MRPT methods as well as into possible approaches for further improving these methods. Calculations are also presented for a simple problem whose divergent traditional MRPT perturbation expansion mimics that commonly encountered when these methods are applied in transition state or bond breaking regions of potential surfaces. (C) 1997 American Institute of Physics. [S0021-9606(97)01941-7].