An external combustion engine containing a working fluid comprising: a burner element for heating the working fluid of the engine; at least one heater head comprising a cylinder wall and defining a working space containing the working fluid; at least one piston for compressing the working fluid, the piston arranged within the cylinder wall of the heater head; a cooler for cooling the working fluid; a crankcase comprising: a crankshaft for producing an engine output; a piston rod connected to the piston; a drive mechanism that converts the linear motion of the piston rod to rotary motion of the crankshaft; and a linear cross-head bearing comprising a journal and a guide, wherein the journal has a first end rigidly attached to the piston rod and a second end attached to the drive mechanism, wherein the guide is located outside the working space, the linear cross-head bearing is a hydrodynamic bearing supplied with lubricating fluid from an annulus on the guide; and the external combustion engine further comprises a rolling diaphragm is mounted to the first end of the journal; characterised in that the length/diameter ratio and radial clearance of the linear cross-head bearing is such that the piston will not contact the cylinder wall of the heater head nor the cooler during operation so that the linear cross-head bearing solely constrains the motion of the piston. a burner element for heating the working fluid of the engine; at least one heater head comprising a cylinder wall and defining a working space containing the working fluid; at least one piston for compressing the working fluid, the piston arranged within the cylinder wall of the heater head; a cooler for cooling the working fluid; a crankcase comprising: a crankshaft for producing an engine output; a piston rod connected to the piston; a drive mechanism that converts the linear motion of the piston rod to rotary motion of the crankshaft; and a linear cross-head bearing comprising a journal and a guide, wherein the journal has a first end rigidly attached to the piston rod and a second end attached to the drive mechanism, wherein the guide is located outside the working space, the linear cross-head bearing is a hydrodynamic bearing supplied with lubricating fluid from an annulus on the guide; and the external combustion engine further comprises a rolling diaphragm is mounted to the first end of the journal; characterised in that the length/diameter ratio and radial clearance of the linear cross-head bearing is such that the piston will not contact the cylinder wall of the heater head nor the cooler during operation so that the linear cross-head bearing solely constrains the motion of the piston. a crankshaft for producing an engine output; a piston rod connected to the piston; a drive mechanism that converts the linear motion of the piston rod to rotary motion of the crankshaft; and a linear cross-head bearing comprising a journal and a guide, wherein the journal has a first end rigidly attached to the piston rod and a second end attached to the drive mechanism, wherein the guide is located outside the working space, the linear cross-head bearing is a hydrodynamic bearing supplied with lubricating fluid from an annulus on the guide; and the external combustion engine further comprises a rolling diaphragm is mounted to the first end of the journal; characterised in that the length/diameter ratio and radial clearance of the linear cross-head bearing is such that the piston will not contact the cylinder wall of the heater head nor the cooler during operation so that the linear cross-head bearing solely constrains the motion of the piston.