The possibility to harden composite materials through producing space charge layers on their surface is considered for the first time. Fullerenes, nanotubes, and other nanostructures with a large electron affinity may be used as the trapping sites for free electrons generating the negative charged layer of the space charge on the hardenable material surface. These nanostructures (modifiers) with a large electron affinity attach the free electrons and thus charge the modifiable material with a positive charge. As the analytical calculations show, the dozens of times modification of the strength characteristics of the composite materials by the space charge layers is possible. The analytical calculations of the resonance bulk percentage of the modifier with the characteristic dimensions of the nanocrystals and the modifier itself being known, have been carried out. According to the analytical calculations, the hardening by molecules of C60 up to104 GPa of crystals of copper and other materials with free electrons can be expected.