  We analyse the stringy gravitational wave background based on the current
algebra $E^{c}_{2}$. We determine its exact spectrum and construct the modular
invariant vacuum energy. The corresponding N=1 extension is also constructed.
The algebra is again mapped to free bosons and fermions and we show that this
background has N=4 (N=2) unbroken spacetime supersymmetry in the type II
(heterotic case).
