Expressions for the energies of the rotational levels associated with a nearly degenerate A1A2 pair of vibronic states in a molecule of symmetry C3v are presented. These expressions take into consideration Coriolis interaction between the levels associated with the A1 vibronic state and the levels associated with the A2 vibronic state. Expressions for the intensities of rotational lines in transitions involving such a nearly degenerate A1A2 pair of vibronic states are also presented. In certain cases transitions involving a (accidentally) degenerate A1A2 pair of vibronic states will have the same appearance as transitions involving a (necessarily) degenerate E vibronic state. A loose analogy between the problem discussed in this paper and the problem of spin uncoupling in a 2Π state of a diatomic molecule is pointed out.