  Purely gravitational pp-waves in AdS backgrounds are described by the
generalised Kaigorodov metrics, and they generically preserve 1/4 of the
maximum supersymmetry allowed by the AdS spacetimes. We obtain 1/2
supersymmetric purely gravitational pp-wave solutions, in which the Kaigorodov
component is set to zero. We construct pp-waves in AdS gauged supergravities
supported by a vector field. We find that the solutions in D=4 and D=5 can then
preserve 1/2 of the supersymmetry. Like those in ungauged supergravities, the
supernumerary supersymmetry imposes additional constraints on the harmonic
function associated with the pp-waves. These new backgrounds provide
interesting novel features of the supersymmetry enhancement for the dual
conformal field theory in the infinite-momentum frame.
