We present a numerical study which explores the nonlinear cascade effect associated with Alfv¿n waves in the fast solar wind. The set of one-dimensional, two-fluid equations describing the solar wind and a power spectrum equation for Alfv¿n waves, as first proposed by Tu et al. [1984>, are solved simultaneously in a self-consistent manner. Both Kolmogorov and Kraichnan cascade functions, which vary as f5/2P3/2 and f3P2, respectively, and considered. For an Alfv¿n wave spectrum at the coronal base, which is flat in the low-frequency range and has a slope of -1 in the high-frequency range, the Kolmogorov cascade function reproduces the Alfv¿n wave spectrum observed beyond 0.29 AU very well. The Kraichnan cascade function, on the other hand, yields a spectrum that is within the 90% confidence level of the observed values. Both cascade functions yield a gradually accelerating fast solar wind in the inner corona, typical of wave acceleration models. The results of this first solar wind model which describes, in a self-consistent manner, the evolution of the wave spectrum and cascade in the inner corona confirm conclusions reached by earlier studies, namely, that the Kolmogorov process produces a stronger cascade effect than the Kraichnan process and seems more relevant for Alfv¿n waves in the fast solar wind, at least beyond 0.29 AU. The approach shows that Alfv¿n waves with periods of hours or shorter, undergo an appreciable evolution from the solar surface to 1 AU, thus implying that their spectrum; hence their total energy flux at the Sun cannot be readily predicted from that observed in interplanetary space. ¿ 1999 American Geophysical Union