1. A method of controlling the breathing cycle of a patient comprising: determining the total resistance R of the patient's lungs; determining the total compliance C of the patient's lungs; determining the alveolar tidal volume V.degree..sub.AT of the patient's lungs; delivering oxygen enriched air to the patient for an inspiration period .tau. of the breathing cycle at an initial pressure RV.degree..sub.AT /.tau. and increasing the pressure to a pressure ##EQU17## at the end of the inspiration cycle; and lowering the pressure to a level below RV.degree..sub.AT /.tau. during an expiration period of the breathing cycle.