This paper deals with three classes of generalized vector quasi-equilibrium problems with or without compact assumptions. Using the well-known Fan-KKM theorems, their existence theorems for them are established. Some examples are given to illustrate our results.Keywords Generalized vector quasi-equilibrium problem · Weak type C x -diagonal quasi-convex and strong type C x -diagonal quasi-convex · Fan-KKM theorem Mathematics Subject Classification (2000) 49K30 · 90C29