A transmission includes a controller being provided with a change-speed stage anticipator. The controller adopts a time, which one of the transmission's gear-mechanism selectors requires in shifting a current change-speed stage to another change-speed stage, as a pre-shift time for selecting the latter change-speed stage. The change-speed stage anticipator operates the one of the gear-mechanism selectors while adopting a temporary change-speed stage as a subsequent change-speed stage when the temporary change-speed stage, which is estimated from a state of vehicle after the pre-shift time, the state of vehicle being relevant to each element of an anticipated change-speed stage group that is made up of one or more of the change-speed stages that can be selected by the one of the gear-mechanism selectors being set on one of the transmission's input shafts that is disconnected from a power source, coincides with an anticipated change-speed stage that corresponds to the pre-shift time.