The paper considers compensation for turbulent distortions of laser beams by an adaptive system including a Hartmann sensor. The control is realized under the conditions of singular points present in the radiation phase profile. To analyze the effect of dislocations on the accuracy of wave front registration, two algorithms of localization of singular points have been developed. The first algorithm is based on analysis of the phase surface of radiation and can be used only in a numerical experiment. In the second algorithm, dislocations are determined as branching points of interference fringes. This algorithm can be implemented experimentally. The accuracy provided by the both algorithms has been compared and the statistics of dislocations on the path has been obtained. The efficiency of phase conjugation was analyzed taking into account the restrictions introduced by the sensor. It is shown that the control loses its stability in the presence of dislocations, and a method is proposed to increase the stability.