By the use of the reversion method certain types of ordinary nonlinear differential equations can be reduced to a set of ordinary linear differential equations which may conveniently be solved by the Laplace transform. The expression for the general member of the linear set is developed and written out in detail for certain illustrative terms. The method is applied to two simple problems for which the answers are exactly known so that some idea may be obtained as to the excellence of the approximations supplied by this method.