The present invention provides a rear wheel steering angle controlling device for vehicles comprising: a rear wheel steering mechanism (5R, 5L) for changing a rear wheel steering angle; a front wheel steering angle detector (9) for detecting a front wheel steering angle (δf); a vehicle velocity detector (10R, 10L) for detecting a vehicle velocity (V); a feedforward rear wheel steering angle control target value setting unit (21) for setting a feedforward control target value (δrFF) of said rear wheel steering angle according to said front wheel steering angle, said vehicle velocity, a steering yaw rate transfer function property (Gγ0) of the vehicle without a rear wheel steering angle control, and a prescribed reference steering yaw rate transfer function property (Gideal); and a controlling device (11) for controlling said rear wheel steering mechanism according to said feedforward rear wheel steering angle control target value; wherein a steady-state property of said reference steering yaw rate transfer function property is configured to be identical to said steering yaw rate transfer function property without said rear wheel steering angle control.