An improved, free-piston, Stirling machine having at least three pistons series connected in an alpha Stirling configuration. Each cylinder is stepped so that it has a relatively larger diameter interior wall and a coaxial, relatively smaller diameter interior wall. Each piston is also stepped so that it has a first component piston having an end face facing in one axial direction and matingly reciprocatable in the smaller diameter cylinder wall and a second component piston having an end face facing in the same axial direction and matingly reciprocatable in the larger diameter, cylinder wall. Improved balancing or vibration reduction is obtained by connecting expansion and compression spaces of a four cylinder in-line arrangement in a 1, 3, 2, 4 series sequence. Three cylinder embodiments provide a highly favorable volume phase angle of 120 DEG and are advantageously physically arranged with three, parallel, longitudinal axes of reciprocation at the apexes of an equilateral triangle.