This paper describes self-excited oscillation caused by coulomb friction of electromagnetic proportion valve. Especially, we focus on a hydraulic system in which electromagnetic proportion and pressure proportion valves are located tandemly. In the system, the coulomb frictional force effects on the displacement direction of the spool of the former valve and the piston is established in the downstream region of the latter valve. Each valve is stable, but, the connection of them causes instability. In this study, we analyze the mechanism of this unstable vibration and then investigate an anti-vibration design method. In analysis, this paper clarifies that the vibration is caused by an elastic deformation delay of the oil in the piston. This delay increases the phase delay of the spool due to the coulomb frictional force. In the design method, we use the describing function method to express phase delay phenomenon due to the coulomb frictional force. The effectiveness of this design method is demonstrated via practical experiment and non-linear simulation results.