We analyze perturbations of linear functionals (both on the real line and on the unit circle) that belong to the Laguerre-Hahn class. In particular, we obtain an expression for the Stieltjes and Caratheodory functions associated with the perturbed functionals, and we show that the Laguerre-Hahn class is preserved. We also discuss the invariance of the class under the Szegö transformation.