Formulas are given for an approximation to the energy values of the levels of the asymmetric rotor when the latter are essentially twofold degenerate. The method of arriving at these formulas follows that described recently, in which the energy matrix is examined under conditions where J→∞. In contrast to the latter method, however, the present approximation considers those levels for which (in the limiting symmetric cases) |K| is very nearly equal to J. With these restrictions, the energy matrix of the asymmetric rotor assumes a form that can be related to that which may be obtained from a perturbed harmonic oscillator.