The transition from spherical to globular and cylindrical equilibrium modifications of micelles in solutions of nonionic surfactants is numerically studied within the framework of the droplet model of molecular aggregates. Two branches of the curve of micelle aggregation work are plotted as a function of aggregation numbers. One of these curves corresponds to the globular micelles; the other, to spherocylindrical micelles. At aggregation numbers corresponding to the limiting spherical packing, both the globules and spherocylinders are transformed into the limiting sphere. It is shown that the ratio between the branches depends on the dimensionless parameter characterizing the ratio of electrostatic and surface contributions to the aggregation work. It is elucidated that, at certain values of this parameter and surfactant monomer concentration in solution, in addition to the maximum in the region of submicellar aggregates for spherical micelles, the second maximum arises on the curve of aggregation work as a function of aggregation numbers in the region of transition to spherocylindrical micelles. The appearance of an additional maximum is shown to be caused by the sum of surface, electrostatic, and concentration contributions to the aggregation work and is not directly related to the conformational contribution to the aggregation work.