Transport moments up to fourth order for convolution-, quasi-, and classical-Fickian dispersion of a conservative tracer are presented and compared. Convolution-Fickian yields a non-Gaussian distribution while quasi- and classical-Fickian result in Gaussian type distributions regardless of the distribution of a stationary velocity field. The first and second central spatial moments are the same for convolution- and quasi-Fickian dispersion, while the third and fourth central moments differ. ¿ American Geophysical Union 1995