Automatic transmission apparatus and straddle-type vehicle equipped with the apparatus

An automatic transmission apparatus (50) has a clutch (44) having drive side and driven side rotators, a detecting device for detecting a clutch relative speed and a decrease rate per unit time of the clutch relative speed, the clutch relative speed being a difference between a rotational speed of the drive side rotator and a rotational speed of the driven side rotator, an actuator (60) for driving the clutch (44), and a control device (90) for controlling the engine (45) and so forth. The control device (90) has an ignition timing retard control unit (96) for executing an ignition timing retard control process for the engine (45) in gear shifting, a threshold value setting unit (92) for setting a threshold value based on the decrease rate, and a return command unit (98) for outputting a command for ending the ignition timing retard control process if the clutch relative speed becomes equal to or less than the threshold value before completing engagement of the clutch.