A heat machine having an external heat source and an external heat sink may be configured as a Stirling engine having a hot pair of cylinder-and-displacer combinations 15 and a cold pair of cylinder-and-displacer combinations 16 though advantageously two pairs of hot combinations 15 and two pairs of cold combinations 16 are provided, arranged mutually at right angles. Mechanisms 20 associated with the hot and cold displacers controls the movement thereof to be truly sinusoidal and are contained within casings 21. The pressure in the working fluid spaces remote from the mechanisms 20 and also the pressure in the casings 21 is monitored and compared, and then is controlled such that the casing pressure is slightly less than the minimum working fluid pressure in the working fluid spaces. The relative phase of the two mechanisms 20 associated respectively with the hot displacers and the cold displacers is adjustable (28,29,30,31; and FIG. 4).