We study the gravitational waves in the 10-dimensional target space of the superstring theory. Some of these waves have unbroken supersymmetries. They consist of Brinkmann metric and of a 2-form field. Sigma-model duality is applied to such waves. The corresponding solutions we call dual partners of gravitational waves, or dual waves. Some of these dual waves upon Kaluza-Klein dimensional reduction to 4 dimensions become equivalent to the conformo-stationary solutions of axion-dilaton gravity. Such solutions include dilaton extreme black holes, axion-dilaton Israel-Werner-Perjes-type spacetimes and extreme charged axion-dilaton Taub-Nut solutions. The unbroken supersymmetry of the gravitational waves transfers to the unbroken supersymmetry of axion-dilaton IWP solutions. More general supersymmetric 4-dimensional configurations derivable from 10-dimensional waves are described.