We apply the nonlocal condensate formalism to construct generalized sum rules (including O(alpha(s))-radiative corrections) for pi-, rho- and rho '-meson wave functions of twist 2. Besides, we predict the lepton decay constant f(rho ') and estimate the mass of rho '-meson. For all these mesons we obtain the first 10 moments of longitudinal wave functions, suggest the models for them and discuss their properties. We consider the peculiarities of the QCD sum rules with nonlocal condensates for transverse rho- and b(1)-meson wave functions. These results are compared with those found by Ball and Braun and by Chernyak and Zhitnitsky. (C) 1998 Published by Elsevier Science B.V. All rights reserved.