Abstract: The paper studied two kinds of parametric well-posedness for weak vector equilibrium problems in real Banach spaces. It established some metric characterizations of uniquely well-posedness and well-posedness for the problems. It proved that under suitable conditions, the uniquely well-posedness is equivalent to the existence and uniqueness of solutions. Finally, it gave sufficient conditions to well-posedness in finite dimensional space.

Key words: weak vector equilibrium problems, parametric well-posedness, metric characterizations