  We analyze the coset model $(E_2^c \ti E_2^c)/E_2^c$ and construct a class of
exact string vacua which describe plane gravitational waves and their duals,
generalizing the plane wave background found by Nappi and Witten. In
particular, the vector gauging describes a two-parameter family of singular
geometries with two isometries, which is dual to plane gravitational waves. In
addition, there is a mixed vector-axial gauging which describes a one-parameter
family of plane waves with five isometries. These two backgrounds are related
by a duality transformation which generalizes the known axial-vector duality
for abelian subgroups.
