  Let $\mathcal A$ and $\mathcal B$ be two closed linear relation acting
between two Banach spaces $X$ and $Y$ and let $\lambda$ be a complex number. We
study the stability of the nullity and deficiency of $\mathcal A$ when it is
perturbed by $\lambda\mathcal B$. In particular, we show the existence of a
constant $\rho>0$ for which both the nullity and deficiency of $\mathcal A$
remain stable under perturbation by $\lambda\mathcal B$ for all $\lambda$
inside the disk $\vert \lambda\vert <\rho$.
