  We use an argument of Romans showing that every Virasoro construction leads
to realizations of $W_3$, to construct $W_3$ realizations on arbitrary affine
Lie algebras. Solutions are presented for generic values of the level as well
as for specific values of the level but with arbitrary parameters. We give a
detailed discussion of the $\aff{su}(2)_\ell$-case. Finally, we discuss
possible applications of these realizations to the construction of $W$-strings.

High Energy Physics - Theory