A multiple clutch transmission control apparatus performs gear changing smoothly by improving clutch torque control precision, without reducing the speed of gear changing, in a vehicle or the like including a multiple clutch transmission. With this control apparatus, a control unit switches the transmission gear from the previous gear to the next gear by changing the torque transfer path by controlling the first clutch and the second clutch in a clutch changeover period. In the clutch changeover period, the control unit changes the torque transfer path by raising the clutch torque capacity of whichever of the first clutch and the second clutch is the next-gear-side clutch to reach a target value, and then lowering the clutch torque capacity of the previous-gear-side clutch.