The NMR pulsed field gradient spin-echo (PFGSE) amplitude M(k,t) is a direct measure of the diffusion propagator of the molecules of a fluid diffusing in the pores of a porous medium. For small values of k = 'yg&, where g is the gradient strength, 6 is the duration of the gradient pulse, and y the gyromagnetic ratio, the PFGSE amplitude gives the diffusion coefficient o(t). The exact short-time diffusion coefficient, D(t)/&, = 1 -(4m,S)/ (9& &?) -D&L!V(12 5) + ptS/6Y,, provides an important method for determining the surface to pore-volume ratio S/V,. Here the mean surface curvature H = (l/R1 + l/R&. Combining early II(f) with the magnetization decay one obtains the surface relaxivity p. The long-time effective diffusion constant derived from PFGSE gives information on the tortuosity of the connected space. The diffusion coefficient measured by PFGSE equals that derived from electrical conductivity only when p = 0. Exact solutions with partially absorbing boundary conditions for a periodic structure are used to illustrate the influence of p on the diffusion coefficient. M(k,t) can be well represented by a convolution of the structure factor of the connected pore space with an appropriate Gaussian propagator. This ansatz provides a model-independent way of obtaining the structure factor.