Three types of nonlinear ratemeters are described and the differential equation for the system response is developed in each case. Several methods of solving these nonlinear differential equations are discussed and their practical application compared for typical input functions. The experimental determination of the time constant-output relation for one of the ratemeters is described and comparisons made of computed and recorded outputs for these input functions with this instrument. The excellent agreement indicates that the analysis provides a valid basis for the development of correction procedures for the response time distortion of nonlinear ratemeters.