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The possibilities of generalizing the dispersion equations of flow through porous media are investigated. Based on the hypothesis (‘Bear's hypothesis’) that only that part of each velocity component is of significance which is either parallel or normal to the mean flow direction, the general form of the dispersion is deduced. The dispersivity becomes a tensor of the fourth rank. It has such symmetry properties that it contains only 36 instead of 81 independent components in the general case of an anisotropic porous medium. In isotropic media there are only two dispersivity constants. The latter result had already been deduced by Nikolaevskii. The connection of the dispersivity tensor with a tensor which had previously been constructed by Bear is demonstrated.

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