  The elements of $O(d,d,\Z)$ are shown to be discrete symmetries of the space
of curved string backgrounds that are independent of $d$ coordinates. The
explicit action of the symmetries on the backgrounds is described. Particular
attention is paid to the dilaton transformation. Such symmetries identify
different cosmological solutions and other (possibly) singular backgrounds; for
example, it is shown that a compact black string is dual to a charged black
hole. The extension to the heterotic string is discussed.
