In servo systems, the dynamic characteristics may not only differ between axes but may also vary with moving directions for a single axis. The direction dependent characteristics would result in additional tracking or positioning error and degrade the performance of the system. In this paper, relay feedback tests are successfully applied to identify the dynamic characteristics in servo systems. A time-domain method is used to analyze the relay feedback other than the conventional describing function (DF) method. The time-domain method utilizes the same oscillation parameters (oscillation amplitude and half period) as the DF method for system identification. However, the time-domain method takes several advantages: First, the direction dependent characteristics of the system can be properly revealed; second, no approximation is made in this method, so that the exact expressions of the amplitudes and the periods of the limit cycles under relay feedback can be derived. A feedforward compensator is then designed using the estimated values of the system parameters. Simulation results show that the identification results through the time-domain method are more accurate than the DF method and are more robust under different relay parameters. Real time experiments show that the feedforward compensator designed by the proposed method compensates disturbances related to the direction and hence improves the tracking and positioning performance of the servo system.