  We describe an infinite-dimensional algebra of hidden symmetries for the
self-dual gravity equations. Besides the known diffeomorphism-type symmetries
(affine extension of w(infinity) algebra), this algebra contains new hidden
symmetries, which are an affine extension of the Lorentz rotations. The full
symmetry algebra has both Kac-Moody and Virasoro-like generators, whose
exponentiation maps solutions of the field equations to other solutions.
Relations to problems of string theories are briefly discussed.
