  The widely used nonperturbative wave functions and distribution functions of
QCD are determined as matrix elements of light-ray operators. These operators
appear as large momentum limit of nonlocal hadron operators or as summed up
local operators in light-cone expansions. Nonforward one-particle matrix
elements of such operators lead to new distribution amplitudes describing both
hadrons simultaneously. These distribution functions depend besides other
variables on two scaling variables. They are applied for the description of
exclusive virtual Compton scattering in the Bjorken region near forward
direction and the two meson production process. The evolution equations for
these distribution amplitudes are derived on the basis of the renormalization
group equation of the considered operators. This includes that also the
evolution kernels follow from the anomalous dimensions of these operators.
Relations between different evolution kernels (especially the Altarelli-Parisi
and the Brodsky-Lepage) kernels are derived and explicitly checked for the
existing two-loop calculations of QCD. Technical basis of these results are
support and analytically properties of the anomalous dimensions of light-ray
operators obtained with the help of the $\alpha$-representation of Green's
functions.
