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In some semiconductors the conduction band system has two minima separated by only a small energy, and the lower minimum has associated with it a smaller electron effective mass than the upper minimum. At high electric fields it should be possible to transfer electrons to the upper minimum where they will have a lower mobility. The conductivity of a homogeneous crystal bar can therefore decrease as the field is increased, and it is conceivable that a differential negative resistance could be obtained. The conditions needed for obtaining negative resistance are examined, and calculations made for GaSb and semi-insulating GaAs. It appears that negative resistances should be observable in both these materials.