AdS pp-waves

We obtain the pp-waves of D=5 and D=4 gauged supergravities supported by $U(1{)}^3$ and $U(1{)}^4$ gauge field strengths respectively. We show that generically these solutions preserve 1/4 of the supersymmetry, but supernumerary supersymmetry can arise for appropriately constrained harmonic functions associated with the pp-waves. In particular it implies that the solutions are independent of the light-cone coordinate $x^{+}$. We also obtain the pp-waves in the Freedman-Schwarz model.