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A semi-classical theory of higher order centrifugal distortion corrections in asymmetric rotor molecules is developed, with special consideration of nonlinear XYX-type molecules. While in recent papers devoted to the formulation of the general quantum mechanical theory of this problem all the terms of a given power of the angular momentum operators are simultaneously considered at the corresponding stage of the approximation procedure, the semi-classical theory stresses rather the interrelations between the different orders of approximation, and gives some insight into the overall convergence pattern of the expansions used. Two limiting cases are considered in detail: (a) the symmetric rotor limit $(J\approx K\gg 1)$, and (b) the ``$asymptotic″1$ limit $(J\gg K\sim 1)$. Consideration of these two limiting cases leads to estimates of critical values of the rotational quantum numbers K and J, respectively. For values of K and J exceeding these critical values the expansion procedures used cannot be expected to lead to meaningful results. The semi-classical theory permits reproduction of some of the formulas of the general quantum mechanical theory in a relatively simple way, and leads further to the derivation of a number of formulas which might be useful as a guide towards future developments of the general theory. A correlation of the results of the semi-classical theory with the corresponding results of the general theory is attempted where possible.