A new type of negative resistance effect is described. This effect arises from the properties of hot electrons in a material with a band structure consisting of several nonspherical valleys. A semiempirical theory is developed for this effect, based on a model for hot-electron behavior which assumes (1) that the mobility and "temperature" of the electrons in each valley are determined uniquely by specifying the power delivered to the electrons, (2) that the mobility in each valley has the anisotropy of the effective-mass tensor for that valley, and (3) that the intervalley scattering time depends only on the "temperature" of the valley from which the carriers are scattered and not on that of the valley to which they scatter. This results in a criterion for the occurrence of the negative resistance which is applied to the case of n-germanium at 78°K where the parameters needed can be evaluated from other experimental data. It is shown that, under appropriate conditions, the negative resistance should occur in this material. Experimental evidence is then presented for its existence.