The　conceptions　of　(generalized)　Tykhonov　well-posedness　for　generalized　vector　quasi-equilibrium　problems,　(generalized)　Hadamard　well-posedness　for　parametrically　generalized　vector　quasi-equilibrium　problems　and　(generalized)　Tykhonov　well-posedness　for　parametrical　system　of　generalized　vector　quasi-equilibrium　problems　are　introduced.　The　metric　characterizations　and/or　sufficient　criteria　of　the　proposed　well-posedness　are　presented,　and　the　relations　between　(generalized)　Tykhonov　well-posedness　for　generalized　vector　quasi-equilibrium　problems　and　that　for　constrained　minimizing　problems　are　discussed.　Finally,　the　relations　among　several　types　of　the　well-posedness　are　exhibited　in　detail.