  In this work we address the question of proving the stability of elliptic
2-periodic orbits for strictly convex billiards. Eventhough it is part of a
widely accepted belief that ellipticity implies stability, classical theorems
show that the certainty of stability relies upon more fine conditions. We
present a review of the main results and general theorems and describe the
procedure to fullfill the supplementary conditions for strictly convex
billiards.
