A drive train for the sleeve of a sleeve valve engine has a pair of drives imparting compound motion to the sleeve which gives improved port opening and closing. One drive uses a engine driven first gear to give eccentric motion to the sleeve by a cam and follower. The other drive uses an engine driven second gear to give a small simultaneous rotation to the sleeve by an eccentric pin during a split sleeve. One drive allows axial response without preventing rotational response from the other drive. The sleeve path allows tall narrow ports which allow the piston rings to be nearer the piston crown and this reduces emissions.