  In this paper, a Lagrangian perturbation theory for the second order
treatment of small disturbances of the event horizon in Schwarzchild black
holes is introduced. The issue of gauge invariance in the context of general
relativistic theory is also discussed. The developments of this paper is a
logical continuation of the calculations presented in \cite{Vega+Poisson}, in
which the first order coordinate dependance of the intrinsic and exterinsic
geometry of the horizon is examined and the first order gauge invariance of the
intrinsic geometry of the horizon is shown. In context of second order
perturbation theory, It is shown that the rate of the expansion of the
congruence of the horizon generators is invariant under a second order
reparametrization; so it can be considered as a measure of tidal perturbation.
A general expression for this observable, which accomodates tidal
perturbations, is also presented.
