  In this note we prove in the nonlinear setting of $CD(K,\infty)$ spaces the
stability of the Krasnoselskii spectrum of the Laplace operator $-\Delta$ under
measured Gromov-Hausdorff convergence, under an additional compactness
assumption satisfied, for instance, by sequences of $CD^*(K,N)$ metric measure
spaces with uniformly bounded diameter. Additionally, we show that every
element $\lambda$ in the Krasnoselskii spectrum is indeed an eigenvalue, namely
there exists a nontrivial $u$ satisfying the eigenvalue equation $- \Delta u =
\lambda u$.
