The object of the study is an exoskeleton of the lower extremities with a rigid structure of the power frame, which has 7 degrees of freedom. The movement of the exoskeleton in the sagittal plane is considered with the assumption of symmetrical movement of the right and left legs. The aim of the study is to develop a mathematical model of the dynamics of the exoskeleton, taking into account the forces of viscous friction in the joints. The equations of motion are obtained under the condition that there is no slippage of the points of contact with the supporting surface. Based on the results of numerical simulation, the control moments were obtained, which must be created by the drives to provide program movement.