  Let $G$ be a simple graph on $n$ vertices and let $J_{G,m}$ be the
generalized binomial edge ideal associated to $G$ in the polynomial ring
$K[x_{ij}, 1\le i \le m, 1\le j \le n]$. We classify the Cohen-Macaulay
generalized binomial edge ideals. Moreover we study the unmixedness and
classify the bipartite and power cycle unmixed ones.
