Two-dimensional problems of dislocations in elastic micropolar media are considered. In the case of a plane state of strain, the compatibility equations may be divided into two mutually independent systems of equations. The first system is connected with the vectors of displacement u (u//1, u//2, 0) and rotation phi (0,0 phi //3), the second with vectors u equals (0,0, u//3) and phi ( phi //1, phi //2, 0). The equations of compatibility for the both cases are written in terms of stresses. The cases of edge, screw and wedge dislocations are considered in detail.