An intermesh engagement device comprising: an engagement mechanism that is an intermesh mechanism including a piece and a sleeve, the engagement mechanism being configured to be engaged or released as the piece and the sleeve relatively move in an axial direction; a moving member configured to move in the axial direction; an actuator configured to apply a thrust to the moving member in a direction in which the sleeve is engaged with the piece; a transmission spring interposed between the moving member and the sleeve, the transmission spring being configured to transmit the thrust of the actuator from the moving member to the sleeve; a return spring configured to apply an urging force to the moving member in a direction opposite to the direction of the thrust of the actuator; a stopper provided at a maximum stroke position of the moving member, the stopper being configured to stop the moving member; and an electronic control unit (74, 86) configured to control the actuator, the intermesh engagement device characterized in that the electronic control unit (74, 86) is configured to: (i) at the time when the engagement mechanism is engaged, execute first control for setting the thrust of the actuator to a thrust in a first region, and (ii) when a halfway stopped state of the engagement mechanism has occurred through the first control, execute second control for setting the thrust of the actuator to a thrust larger than the thrust in the first control, the first region being a range in which the thrust of the actuator at a stroke position of the moving member is larger than the urging force of the return spring, and the first region being a range in which the thrust of the actuator is smaller than the sum of the urging force of the return spring at the stroke position and a maximum urging force that is generated by the transmission spring at the stroke position in the case where movement of the sleeve is restricted. an engagement mechanism that is an intermesh mechanism including a piece and a sleeve, the engagement mechanism being configured to be engaged or released as the piece and the sleeve relatively move in an axial direction; a moving member configured to move in the axial direction; an actuator configured to apply a thrust to the moving member in a direction in which the sleeve is engaged with the piece; a transmission spring interposed between the moving member and the sleeve, the transmission spring being configured to transmit the thrust of the actuator from the moving member to the sleeve; a return spring configured to apply an urging force to the moving member in a direction opposite to the direction of the thrust of the actuator; a stopper provided at a maximum stroke position of the moving member, the stopper being configured to stop the moving member; and an electronic control unit (74, 86) configured to control the actuator, the intermesh engagement device characterized in that the electronic control unit (74, 86) is configured to: (i) at the time when the engagement mechanism is engaged, execute first control for setting the thrust of the actuator to a thrust in a first region, and (ii) when a halfway stopped state of the engagement mechanism has occurred through the first control, execute second control for setting the thrust of the actuator to a thrust larger than the thrust in the first control, the first region being a range in which the thrust of the actuator at a stroke position of the moving member is larger than the urging force of the return spring, and the first region being a range in which the thrust of the actuator is smaller than the sum of the urging force of the return spring at the stroke position and a maximum urging force that is generated by the transmission spring at the stroke position in the case where movement of the sleeve is restricted. (i) at the time when the engagement mechanism is engaged, execute first control for setting the thrust of the actuator to a thrust in a first region, and (ii) when a halfway stopped state of the engagement mechanism has occurred through the first control, execute second control for setting the thrust of the actuator to a thrust larger than the thrust in the first control, the first region being a range in which the thrust of the actuator at a stroke position of the moving member is larger than the urging force of the return spring, and the first region being a range in which the thrust of the actuator is smaller than the sum of the urging force of the return spring at the stroke position and a maximum urging force that is generated by the transmission spring at the stroke position in the case where movement of the sleeve is restricted.