We develop a general framework for analyzing the effects of restricted geometries and inhomogeneous (nonuniform-gradient) magnetic fields on the relaxation of nuclear magnetization. The formalism naturally separates the effects of radio-frequency pulses by introducing the field scattering kernel F(t)equivalent to<[B(t)-B(0)](2)> which captures all the interactions of the diffusing spins with the inhomogeneous field and with the confining walls. F(t) is the fundamental building block in the computation of the magnetization in any sequence of pulses. We use it to derive explicit formulas for the attenuation of the echoes of a general coherence pathway and thus arbitrary pulse trains. The short-time and long-time results, proved rigorously, are model-independent and hold for arbitrary geometries, both closed, such as a single cell or pore, and open, such as a connected porous medium. In open geometries, we compute the magnetization for all times, using a model form of the time-dependent diffusion coefficient. We apply our formalism to a few common sequences and study in detail the stimulated-echo (STE) and the Carr-Purcell-Meiboom-Gill (CPMG). We find that the STE is much more sensitive to the effects of restriction than the CPMG and that its long-time attenuation will be less than that of the CPMG, in sharp contrast to the free-diffusion behavior. (C) 2003 American Institute of Physics.