  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.
