A pair of quasi-definite linear functionals {u$_{0}$, u$_1$} is a generalized $Delta$-coherent pair if monic orthogonal polynomials (equation omitted) relative to u$_{0}$ and u$_1$, respectively, satisfy a relation (equation omitted) where $sigma$$_{n}$ and T$_{n}$ are arbitrary constants and $Delta$p = p($chi$＋1) - p($chi$) is the difference operator. We show that if {u$_{0}$, u$_1$} is a generalized $Delta$-coherent pair, then u$_{0}$ and u$_{1}$ must be discrete-semiclassical linear functionals. We also find conditions under which either u$_{0}$ or u$_1$ is discrete-classical.ete-classical.