  A covariant, global, variational framework for perturbations in field
theories is presented. Perturbations are obtained as vertical vector fields on
the configuration bundle and they drag, exactly, solution into solutions. The
flow of a perturbation drags solutions into solutions and the dragged perturbed
solutions can be expanded in a series with respect to the flow parameter, hence
it contains perturbations at any order. Mechanics is included as a special
case. As a simple application, we recover the well-known discussion about
stability of geodesics on a sphere $S_2$.
