Summary: We give a stability result for the solution of a two-dimensional elliptic problem with Neumann boundary conditions \[ \begin{cases} -\Delta u_\Omega+ u_\Omega= f\quad &\text{in }\Omega,\\ {\partial u_\Omega\over\partial n}= 0\quad &\text{on }\partial\Omega\end{cases} \] with respect to the geometric domain variation. The perturbations are given in the Hausdorff topology and the stability holds if two conditions are satisfied: the number of the connected components of the complement of the variable domain is uniformly bounded and the Lebesgue measure is stable.