A model is presented to explain the radial evolution of the power spectra of interplanetary Alfv¿nic fluctuations found by Bavassano et al. (1982a) based on the magnetic field data of Helios 1 and 2. It is assumed in this model that Alfv¿nic fluctuations represent an asymmetric state of MHD turbulence in which most of the fluctuations are in the Alfv¿nic wave mode propagating outward from the sun, with a small part of the fluctuations in the wave mode propagating inward. There is weak nonlinear interaction between the two modes. It is also asumed that the turbulence will not become dissociated from the sources that create the waves propagating inward and that the weak nonlinear interaction will remain between 0.3 AU and 1 AU. The nonlinear interaction results in an energy cascading process. Both the effects of the cascadeing process and the effects of the slow variation of the solar wind on the outward propagating waves determine the radial evolution of the power spectra. Starting with the magnetohydrodynamic equations and deriving the equations governing fluctuations and correlation moments, we finally get an equation which describes the power spectrum. We present an analytic solution. The radial evolution of the power spectra of the fluctuations given by the analytical solution, from 0.29 AU to 0.87 AU, is in agreement with the observation of Helios 1 and 2 in the following aspects: (1) The spectral slope increases (in absolute value) for the frequency range lower than 2.5¿10-3 Hz while the slope remains almost unchanged for the frequency range higher than 10-1.5 Hz. (2) The radial gradient of the power spectrum densities increases with increasing frequency. The dissipation length remains nearly unchanged for the frequency range f>10-2 Hz. (3) The radial variation of ⟨b2⟩ is approximately r-3.56. (4). The ratio of ⟨b2⟩/B02 is nearly a constant.