We propose minimization algorithms RMSProp and MOMENTUM with step adaptation. In contrast to the known methods of step adaptation used in variations of the stochastic gradient method, in the proposed step adaptation method, only the structural characteristics of the topology of level surfaces are used. The principle of the step adaptation scheme used in our work is based on the reproduction of the state where the descent direction and the new gradient are found with an exact one-dimensional descent. In the exact one-dimensional descent, the angle between these directions is right. In case of inexact descent, the step is adjusted according to the following rule: if the angle between the direction of descent and the new gradient is obtuse, then the step is too large and should be reduced; if the angle between the direction of descent and the new gradient is acute, then the step should be increased. When using this rule, the step adaptation does not use the characteristics of the gradient values, only the directions of the normals of the tangent hyperplanes to the level surface are used. As our computational experiment has shown, in problems of minimizing functions with noise, the algorithms under study are practically equivalent. For problems with curved ravines, the RMSProp and MOMENTUM algorithms with step adaptation are more preferable. Moreover, all algorithms enable us to obtain a solution with a tenfold norm gradient of noise uniformly distributed in a multidimensional ball. On the test problem of model approximation from initial data, the RMSProp and MOMENTUM algorithms with step adaptation make it possible to obtain a solution on small data packets for calculating the gradient. At the same time, RMSProp turns out to be more effective than the MOMENTUM algorithm.