  We introduce a pair of novel difference equations, whose solutions are
expressed in terms of Racah or Wilson polynomials depending on the nature of
the finite-difference step. A number of special cases and limit relations are
also examined, which allow to introduce similar difference equations for the
orthogonal polynomials of the $ _3 F_2$ and $ _2 F_1$ types. It is shown that
the introduced equations allow to construct new models of exactly-solvable
quantum dynamical systems, such as spin chains with a nearest-neighbour
interaction and fermionic quantum oscillator models.
