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Fe-B and Fe-P amorphous alloys exhibit Invar characteristics in a wide temperature range below the Curie temperature, as well as a large high-field susceptibility and a pronounced forced volume magnetostriction. It should be noted that magnetic moment per Fe atom of these alloys does not increase monotonically with decreasing metalloid in contrast to the charge transfer model. The magneto-volume effects are very similar to those of Fe-Ni crystalline Invar alloys and they are explained by Wohlfarth's theory on very weak ferromagnets. Fe-base amorphous alloys also exhibit a large linear magnetostriction and an extremely large ΔE effect, and, above all, for Fe-B and Fe-P amorphous alloys show approximate temperature independence of Young's modulus below the Curie temperature, i.e., Elinvar characteristics. Due to the temperature independence of shear modulus, furthermore, the compressibility should be almost independent of the temperature. These peculiar elastic properties are very different from those of Fe-base crystalline Invar alloys. It is important from the practical point of view that these amorphous alloys have simultaneously Invar and Elinvar characteristics over a wide temperature range.