Abstract: We find the asymptotics of the eigenpairs of the Dirichlet and Neumann spectral problemsfor the Laplace operator in a domain separated by several partitions with holes of small diametersand splitting into several independent cells in the limit as the diameters tend to zero. Usingasymptotic methods for singularly perturbed domains, we study the splitting of a multipleeigenvalue of the limit problems, for example, the zero eigenvalue under the Neumann boundaryconditions, and the localization of the eigenfunction in the case of a simple eigenvalue.