A near isothermal machine for compressing or expanding gas having a piston in a main cylinder with a heat absorbing and releasing structure attached thereto. The main cylinder contains a substantially constant volume of liquid maintained at a substantially constant temperature and a variable volume of gas, the gas temperature being controlled to substantially the same temperature as the liquid by the movement with the piston of the heat absorbing and releasing structure. A compensator is provided to compensate for variations in the level of liquid as the piston moves in the main cylinder.