They're contained.

I've built a Jan Ridders' Coffee Mug engine and the design has no valves. Also have looked at a variety of other designs and none of them had valves either. In theory the same air is used over and over again; it's expanding and contacting within a closed cycle that works the piston.

Possibly a full size engine would need a valve to stop a vacuum forming as it cooled down due to some air having leaked out whilst hot. I think small engines leak enough on their own to equalise pressures without needing a valve.

The engines work more efficiently if the working fluid is pressurised but I've not seen a model engine going to those lengths. That type would need a valve to keep the engine charged, I don't suppose a well-made engine would leak much – the operating pressures are low.

Dave

Just to clarify the "air valve" Ian mentions that is used to govern the speed of the Robinson engines does not draw in new air it is simply sucked into the path of the contained air as it moves from one cylinder to the other restricting the flow rate and therefore speed.