The theory for the perpendicular diffusion of cosmic rays is not well understood which hampers our understanding of cosmic ray modulation. In this paper, a spherically symmetric cosmic ray modulation model is used to evaluate three different theories for perpendicular cosmic ray diffusion in the ecliptic plane, subject to the limitation of negligible cosmic ray transport in the polar direction. In models for the perpendicular diffusion component, it is assumed that perpendicular diffusion due to large-scale field line wandering dominates resonant perpendicular diffusion. To test these models, observations of anomalous and galactic helium obtained during a time of relatively small latitudinal gradients (1996) are used as a guideline. The spatial dependence of the parallel and perpendicular cosmic ray diffusion coefficients is determined completely theoretically using a promising hydromagnetic model for the transport of combined slab plus two-dimensional turbulence in the solar wind [Zank et al., 1996>. The main result of the paper is that the nonperturbative model [Zank et al., 1998> yields the best results. Its success is determined by the following: (1) a perpendicular correlation length derived from two-dimensional solar wind turbulence that is much larger than the parallel correlation length associated with slab turbulence; (2) a modest radial dependence of the radial diffusion coefficient in the outer heliosphere; and (3) a three interval rigidity dependence of the radial diffusion coefficient in the outer heliosphere with the smallest rigidity dependence in the middle interval and a strong rigidity squared dependence in the other two intervals. The nonperturbative model gives a tentative theoretical basis for the cosmic ray modulation simulations by Moraal et al. [1999>, who found empirically that a similar spatial and three stage rigidity dependence for the radial diffusion coefficient is important for reproducing observed anomalous and galactic cosmic ray spectra. ¿ 1999 American Geophysical Union