The transfer group theory is used to study the nonlinear transport system that follows the ion source. The properties of the transfer group and the method of computing the phase‐space contours, distribution functions, and moments of ion beams are studied. It is shown that the nonlinear element can be used to compensate for the aberration. As an example, a method of improving the quality of the beam extracted from an ion source by means of a nonlinear space‐charge lens is discussed.