  We demonstrate the one-to-one correspondence between reparametrization
invariant effective actions for relativistic p-branes in flat target space and
effective actions for transverse brane perturbations with non-linearly realized
Poincar\'e symmetry. Starting with an action with non-linearly realized
symmetry we construct the corresponding reparametrization invariant action by
introducing St\"uckelberg fields. They combine with the transverse modes to
form a Lorentz vector. The manifest Lorentz symmetry of the reparametrization
invariant action follows directly from the non-linearly realized Lorentz
symmetry of the initial action in terms of the physical modes.
