A nonlinear method has been developed to separate arterial pressure and flow waves into their forward and backward running components. It takes into account nonlinearities arising from the area-pressure relationship as well as convective acceleration. The method is based on the treatment of the Riemann invariants and requires measurements of pressure, flow and diameter at one arterial location. The method has been successfully tested by means of a simulation experiment in which the forward and backward waves were known a priori. It was shown that the new method is significantly more accurate in the predictions of the forward and backward waves when compared to the classical linear method. The new wave separation method was then applied to simulated aortic waves for a) a healthy subject and b) a subject with decreased compliance. Comparison with the classical linear method showed that neglecting nonlinearities leads to an overestimation of the forward and backward pressure wave amplitudes of the order of 5 to 10%.