We study a two-dimensional propagation of Alfv¿nic perturbations within the solar equatorial plane (SEP) in the solar wind with a spiral magnetic field. Analytical solutions within the entire frequency range are derived at large radial distance r. Numerical solutions which smoothly pass through the Alfv¿n critical point rA are also obtained. Since the spiral magnetic field caused by the solar rotation scales as ~r-1 at large r, the velocity and magnetic field perturbations, which are perpendicular to the SEP, remain small relative to the wind parameters in the entire radial range. The frequency criterion for the non-WKB radial scalings of the perturbation variables to appear is (f+m f⊙)2<f2c, where f is the perturbation frequency, f⊙ is the solar rotation frequency, m is the azimuthal wavenumber, and fc is the well-known characteristic frequency determined by the wind parameters. We demonstrate that the process of continuous reflection in a spiral magnetic field and the effect of superposing Alfv¿nic perturbations with various f and m can lead to variations of the relative magnetic field fluctuation, the normalized cross helicity &sgr;c, the Alfv¿n ratio ra, the magnetic perturbation energy density Eb, and the kinetic perturbation energy density Ev, which differ from the predictions of the conventional WKB theory. In particular, the non-WKB radial scalings of the perturbation variables can appear at any timescales with appropriate values of m. The relevance of these results to data analyses on interplanetary fluctuations is discussed, and we emphasize the importance of obtaining fluctuation spectrum with respect to both f and m in the outer heliosphere.