Eight stroke engines

I'm sure there are others, but the first to spring to mind is the Aeromotor pumper from USA (see p24 of the current SEM). I believe the 'extra' strokes are interposed between the exhaust and inlet strokes, during which time the exhaust valve is held open (like a hit-and-miss engine running on low load). This allows thorough scavenging of exhaust products and, probably more importantly, what might be thought of as internal forced air cooling which was sufficient to avoid the need for any external fan.