Several possible mechanisms leading to surface reconstruction are discussed and applied to a description of the 2×1 and 7×7 reconstructions of Si (111) and the 2×1 and 2×8 reconstructions of Ge (111) surfaces. Other types of (111) surface reconstructions such as, for example, those with (n√3)×(n√3) and (6n)×(6n) unit cells, which have been observed experimentally on impurity stabilized surfaces, are also predicted.