Nonperturbative functions that parametrize off-diagonal hadronic matrix ele
ments of the light-cone leading-twist quark operators are considered. These
functions are calculated within the proposed relativistic quark model allo
wing for the nontrivial structure of the QCD vacuum, special attention bein
g given to gauge invariance. Hadrons are treated as bound states of quarks;
strong-interaction quark-pion vertices are described by effective interact
ion Lagrangians generated by instantons. The parameters of the instanton va
cuum, such as the effective radius of the instanton and the quark mass, are
related to the vacuum expectation values of the quark-gluon operators of t
he lowest dimension and to low-energy pion observables. (C) 2000 MAIK "Nauk
a/Interperiodica".