This paper is devoted to sensitivity analysis of eigenvalues of nonsym
metric operators that depend on parameters. Special attention is given
to the case of multiple eigenvalues. Due to the nondifferentiability
(in the common sense) of multiple roots, directional derivatives of ei
genvalues and eigenvectors in parametric space are obtained. Sensitivi
ty analysis is based on the perturbation method of eigenvalues and eig
envectors. The generalized eigenvalue problem and vibrational systems
are also investigated. Strong and weak interaction of eigenvalues are
distinguished and interactions in two- and three-dimensional space are
treated geometrically. It is shown that the strong interaction of eig
envalues is a typical catastrophe. Simple examples that illustrate the
main ideas are presented. The results obtained are important for qual
itative and quantitative study of mechanical systems subjected to stat
ic and dynamic instability phenomena.