A method is developed for calculating the effects of a strong oscillating field on two states of a quantum-mechanical system which are connected by a matrix element of the field. Explicit approximate solutions are obtained for a variety of special cases, and the results of numerical computations are given for others. The effect of an rf field on the J=2-->1 l-type doublet microwave absorption lines of OCS has been studied in particular both experimentally and theoretically. Each line was observed to split into two components when the frequency of the rf field was near 12.78 Mc or 38.28 Mc, which are the frequencies separating the J=1 and J=2 pairs of levels, respectively. By measuring the rf frequency, ν0, at which the microwave lines are split into two equally intense components, one may determine the separation between the energy levels. The measured value of ν0 depends upon the intensity of the rf field and the form of this dependence has been calculated and found to be in good agreement with the experimental results.