  In this paper we showed that under two assumptions we are able to define
interesting functions that we call generalized local coefficients. We showed
that in the quasi-split case generalized local coefficients are up to a
positive constant the same as Shahidi's local coefficients. We provide a proof
that the non quasi-split group $GL_m(D)$, for a central division algebra $D$
satisfies those assumptions. We also showed that generalized local coefficients
satisfy nice properties, like the relation to Plancherel measures and
multiplicativity inherited by that of intertwining operators. Generalized local
coefficients are only defined for representations that are
$(Y,\varphi)$-generic which is a generalization of generic representations in
the quasi-split case. Here $Y$ denotes a nilpotent element in the Lie algebra
of the group and $\varphi$ is a co-character related to $Y$.
