  It is shown that the closure of the infinitesimal symmetry transformations
underlying classical ${\cal W}$ algebras give rise to L$_\infty$ algebras with
in general field dependent gauge parameters. Therefore, the class of well
understood ${\cal W}$ algebras provides highly non-trivial examples of such
strong homotopy Lie-algebras. We develop the general formalism for this
correspondence and apply it explicitly to the classical ${\cal W}_3$ algebra.
