The coupled‐pair many‐electron theory, its linear approximation, and various other approximate coupled‐pair approaches based on the orthogonally spin‐adapted coupled‐pair theory are applied to simple model systems in which the degree of quasidegeneracy can be continuously varied over a wide range. The four‐electron models studied are three ab initio minimum basis set models involving four hydrogen atoms in various spatial arrangements as well as the semiempirical Pariser–Parr–Pople π‐electron model of cis‐butadiene. The results are compared with the exact full configuration interaction results as well as with those obtained with other approximate limited configuration interaction approaches and Davidson's formula estimate, and the effect of quasidegeneracy on various approaches is discussed. We also examine the difference between the correlation energies obtained with the coupled‐pair many‐electron theory and its linear version and discuss the source of these differences and of the breakdown of the latter approximation in the case of very strong quasidegeneracies.