  We characterize symmetry transformations of Lagrangian extremals generating
`on shell' conservation laws. We relate symmetry transformations of extremals
to Jacobi fields and study symmetries of higher variations by proving that a
pair given by a symmetry of the $l$-th variation of a Lagrangian and by a
Jacobi field of the $s$-th variation of the same Lagrangian (with $s<l$) is
associated with an `off shell' conserved current. The conserved current
associated with two symmetry transformations is constructed and, as a case of
study, its expression for invariant Yang--Mills connections on Minkowski
space-times is obtained.
