An intermesh engagement device includes an intermesh engagement mechanism, a moving member, an actuator configured to apply a thrust to a moving member in an engaging direction, a transmission spring configured to transmit the thrust of the actuator from the moving member to a sleeve, a return spring, a stopper, and an electronic control unit configured to control the actuator. The electronic control unit is configured to execute first control for setting the thrust of the actuator to a thrust in a first region, and, when a halfway stopped state has occurred through the first control, execute second control for setting a thrust larger than the thrust in the first control. The first region is a range in which the thrust is larger than an urging force of the return spring and is smaller than the sum of the urging force of the return spring and a maximum urging force of the transmission spring.