Few Cycle Pulse Propagation Paul Kinsler, G.H.C. New Department of Physics, Imperial College, Prince Consort Road, London SW7 2BW, United Kingdom. Phys. Rev. A 67, 023813 (2003) There is a longer version of this at http://arXiv.org/physics/0212016 We present a comprehensive framework for treating the nonlinear interaction of few-cycle pulses using an envelope description that goes beyond the traditional SVEA method. This is applied to a range of simulations that demonstrate how the effect of a $\chi^{(2)}$ nonlinearity differs between the many-cycle and few-cycle cases. Our approach, which includes diffraction, dispersion, multiple fields, and a wide range of nonlinearities, builds upon the work of Brabec and Krausz[1] and Porras[2]. No approximations are made until the final stage when a particular problem is considered. Email: Dr.Paul.Kinsler@physics.org