An analytical investigation has been carried out for the motion of moving element in electro-dynamometer type directional power relay under A.C source. For the more a time dependent kinetic performance of the element can also be deduced for the D.C component in fault current. The results obtained thus for show that, in the relay with stopper, the performance time for the equal D.C and A.C component can be shorten ca. 0.5Hz in comparison with the fact, the performance time exhibits to delay ca. 0.75Hz under the same conditions for the case of the relay without stopper, it appear that these differences of performance times will not give vise any difficultys for the apects of practical case, however, the obtain results can be applicable in the course of the design of the relay.