We discuss In\"on\"u-Wigner contractions of affine Kac-Moody algebras. We
show that the Sugawara construction for the contracted affine algebra exists
only for a fixed value of the level k, which is determined in terms of the
dimension of the uncontracted part of the starting Lie algebra, and the
quadratic Casimir in the adjoint representation. Further, we discuss
contractions of G/H coset spaces, and obtain an affine {\it translation}
algebra, which yields a Virasoro algebra (via a GKO construction) with a
central charge given by dim(G/H).Comment: 11 pages, IMSc/92-2