Following an earlier development of a Fokker-Planck equation (FP) for modeling fractal-scale-dependent transport of solutes in one-dimensional subsurface flow of heterogeneous porous media, this technical note extends the FP to three dimensions, and presents a two-dimensional (2-D) FP by reducing the 3-D FP with the aid of the Dupuit approximation. The 2-D FP is derived by including two fractal dispersivities in the convective-dispersive equation leading to a generalized Feller-Fokker-Planck equation (GFFP) featuring both the generalized Feller equation (GF) and FP. Similarity solutions of the 2-D GFP with two linear-scale-dependent dispersivities are presented which can be used as a kernel in the convolution integral to yield an output on a real timescale, and the input function can be derived by a procedure known as the inverse problem with the aid of a Laplace transform.¿ 1997 American Geophysical Union