A new method for the separation of forward and backward running waves in elastic conduits, with possible extension to the arterial system, has been developed. The mathematical model is based on the one-dimensional flow equations which allow the treatment of non-periodic or transient pressure and flow pulses. The method is fully nonlinear, i.e. no linearizing assumptions are made. The method includes the effects of convective acceleration and pressure-dependent vessel compliance. A first approximation for the fluid friction at the wall is also included. The application of the method requires the knowledge of the elastic properties, the instantaneous pressure and flow, as well as the instantaneous spatial derivatives of pressure and flow. Analysis of simulated data shows good results and suggests that the proposed method, unlike previous quasi-nonlinear and frequency domain methods, can be applied to strongly nonlinear and/or nonperiodic flows. The method predicts that if a linear analysis is applied to a nonlinear system errors arise.