  We argue that one can factorize the difference equation of hypergeometric
type on the nonuniform lattices in general case. It is shown that in the most
cases of q-linear spectrum of the eigenvalues this directly leads to the
dynamical symmetry algebra $su_q(1,1)$, whose generators are explicitly
constructed in terms of the difference operators, obtained in the process of
factorization. Thus all models with the $q$-linear spectrum (some of them, but
not all, previously considered in a number of publications) can be treated in a
unified form.
