MPEJ Volume 5, No.5, 11pp Received: Jan 14, 1999, Revised: May 12, 1999, Accepted: Nov 18, 1999 Y. Lacroix Local perturbations of energy and Kac's return time theorem ABSTRACT: We introduce the notion of local perturbations for normalized energies and study their effect on the level of equilibrium measures. Using coupling technics and Kac's return time theorem, we obtain some $\bar{d}$-estimates for the equilibrium measures. These reveal stability of certain energies under local perturbations. They also show how some weak-$\star$ convergence of equilibrium may be obtained in absence of $\norm_\infty$-accuracy of the energies.