Sufficient bounds are presented on the norm bounded uncertainties for the perturbed eigenvalues to remain in a set of disjointed neighbourhoods of the nominal eigenvalues. For such perturbed eigenvalues, bounds on the corresponding eigenvector perturbations are also presented. The study is used to analyse design methodologies based on eigenstructure assignment with parameter variations in a conrollable pair. The left and right eigenvector perturbation analysis carried out in this paper is useful in the time response analysis of linear uncertain systems.