<p>In this paper, the sensitivity analysis of parametric vector equilibrium problems (for short PVEP) is conducted based on the Fréchet coderivative of a multifunction. Firstly, we formulate the formulas for calculating the Fréchet coderivative of the set-valued gap function related to the (PVEP). By estimating the Fréchet subdifferential of the set-valued gap function, we present the precise expression of the Fréchet subdifferential associated with the perturbed map for (PVEP). Moreover, we obtain the Fréchet subdifferential associated with the perturbed map for the parametric vector optimization problems (for short PVOP). Finally, we provide several examples to demonstrate the obtained results.</p>