The motivation for this paper is the fact that in practice, the parameters of a power system are only approximately known. The paper discusses the sensitivity of eigenvalues in terms of state matrix entry changes (model uncertainty) and parameter changes (parameter uncertainty). The concepts of asymptotic stability robustness for model and parameter uncertainty are presented. Two indexes derived from eigenvalue sensitivity matrices are suggested to measure eigenvalue sensitivity and asymptotic small-signal stability robustness. As an example, the sensitivities of the electromechanical modes of a 9-machine system are analyzed. The results show lack of asymptotic stability robustness for both model and parameter uncertainties. The paper shows that lack of asymptotic stability robustness is a trend of actual multimachine power systems because too small stability margins and large eigenvalue sensitivities occur simultaneously.