A hybrid vehicle is taught herein in which a clutch is disposed between an engine and a motor/generator and disengagement of the clutch is controlled hi a coasting drive while dragging the engine. A drive controller engages the clutch so that the vehicle coasts while dragging the engine at a tune of coasting deceleration. While coasting, when the stepped transmission of the hybrid vehicle downshifts, the clutch is disengaged during the downshift.