In the paper a new approach to the air standard cycles of piston combustion engines based on the First and the Second Laws of Thermodynamics has been presented. It has been found that a certain entropy increase during the heat addition is required for the cyclic operation of piston engine. It is dependent on compression ratio and may not be neglected while analyzing the air standard cycles. Consequently, compression ratio, amount of heat added to the working gas and the way of heat addition are interdependent. Taking this into consideration an essential theory of piston combustion engines has been developed and the relationships for the efficiencies of air standard cycles have been completed. Also, an air standard cycle of the engine coupled to a turbine and equations for its efficiency have been discussed.The presented analysis leads to more comprehensive insight into engine operation than the methods outlined in the references.