A high order of thermal efficiency is achieved in a steam engine or expander having a piston clearance that approximates zero together with a negligible amount of compression, such that pressure in the clearance volume approximates ambient pressure, i.e. atmospheric or condenser pressure as the case may be at the end of the piston return stroke when the clearance is essentially zero. These two provisions working together simultaneously provide a method and apparatus which constitute a new engine apparatus and Rankine operating cycle that can be referred to as “zero clearance with zero compression”. The invention also provides an improved steam admission valve assembly that can be operated either automatically responsive to piston movement or by means of a cam shaft and cam or electrically by means of a solenoid that provides an intermittent magnetic field for operating one or more valves. A biphasic exhaust system is described in which a piston operated valve opens to exhaust steam in a primary phase at or near maximum displacement, and in a secondary phase an auxiliary, normally open exhaust valve facing the top of the piston permits virtually all residual steam to be exhausted through the approximate end of the piston return stroke after which it is closed by the piston, by a lifter on the piston or by the cam and finally held closed during the power stroke by a fresh charge of steam injected through the steam admission valve into the clearance volume as it approaches zero.