Wilson, Jankowski, and Paldus have recently applied nondegenerate many‐body perturbation theory (MBPT) to simple models, in which the degree of quasidegeneracy could be varied continuously, and concluded that the nondegenerate theory was applicable even near degeneracy. The error in their results changes, however, considerably with geometry, leading to an incorrect potential surface. An extension of their calculations shows convergence even at exact degeneracy (square planar H4). It is shown here that the apparently good convergence is due to the suppression of the large (infinite at exact degeneracy) component of the perturbation energy in low order by the way the Hamiltonian is partitioned. This component will, however, resurface at higher orders, leading to slow convergence or even divergence. The low‐order sum of the perturbation series is not very meaningful, depends strongly on details of the zero‐order Hamiltonian, and yields, in general, incorrect potential surfaces. Multireference MBPT eliminates these problems.