The transport and diffusion equations appropriate for performing neutronic and photonic calculations in toroidal geometry are derived. This geometry is an important one in current conceptual designs of controlled thermonuclear reactors. It is shown that for an azimuthally independent problem, the toroidal diffusion equation can be cast into the standard r-θ cylindrical equation by appropriately redefining the diffusion coefficient, absorption cross section, and external source. A Fourier expansion of the diffusion equation to obtain the theta dependence of the flux is shown to have the same truncation properties as those associated with the spherical harmonics method. A more useful expansion is one in inverse powers of the aspect ratio of the toroidal system. An idealized problem is solved analytically to obtain the first-order correction term arising from the overall curvature of the toroidal system. For an aspect ratio of three, typical of Tokamak fusion reactors now under consideration, this result indicates that local errors in the flux in excess of 15% can arise if the toroidal character of the geometry is neglected.