Spin echo signal attenuation by diffusion is examined for coherence evolution in the course of ordinary pulsed gradient spin echoes and for nonlinear evolution in the presence of a spatially modulated demagnetizing field. It is shown, that, for given field gradient pulse widths (or equivalently for a given gradient strength), echo attenuation by diffusion is much more efficient for nonlinear echoes than for Hahn echoes. Remarkably, in the case of nonlinear echoes the refocusing process is spoiled by diffusion not only during the gradient intervals but also thereafter. The effect of displacements occurring in the gradient intervals is enhanced according to the order of the nonlinear echo the pulse sequence is adjusted for. A second attenuation mechanism takes place after the gradient pulses due to displacements in the presence of the spatially modulated demagnetizing field. This effect even occurs when the gradient intervals are too short to contribute. A complete formalism is presented describing all features of the test experiments. It is shown that nuclear magnetic resonance diffusometry based on nonlinear echo signals permits one to measure small diffusion coefficients with moderate field gradients. Nonlinear echo experiments demonstrate that the coherence pathway dominating by far is of a purely single-quantum nature. (C) 2000 American Institute of Physics. [S0021-9606(00)00312-3].