  We show that the classical equations of motion of the low-energy effective
field theory describing the massless modes of the heterotic (or type I) string
admit two classes of supersymmetric self--dual backgrounds. The first class,
which was already considered in the literature, consists of solutions with a
(conformally) flat metric coupled to axionic instantons. The second includes
Asymptotically Locally Euclidean (ALE) gravitational instantonic backgrounds
coupled to gauge instantons through the so--called ``standard embedding''. Talk
given by F.Fucito at the XI SIGRAV meeting, Trieste, September 27-30, 1994
