  Applications of perturbative QCD to deeply virtual Compton scattering and
hard exclusive meson electroproduction processes require a generalization of
usual parton distributions for the case when long-distance information is
accumulated in nonforward matrix elements < p'| O(0,z) | p > of quark and gluon
light-cone operators. In our previous papers we used two types of
nonperturbative functions parametrizing such matrix elements: double
distributions F(x,y;t) and nonforward distribution functions F_\zeta(X;t). Here
we discuss in more detail the double distributions (DD's) and evolution
equations which they satisfy. We propose simple models for F(x,y;t=0) DD's with
correct spectral and symmetry properties which also satisfy the reduction
relations connecting them to the usual parton densities f(x). In this way, we
obtain self-consistent models for the \zeta-dependence of nonforward
distributions. We show that, for small \zeta, one can easily obtain nonforward
distributions (in the X > \zeta region) from the parton densities: F_\zeta
(X;t=0) \approx f(X-\zeta/2).
