  A class of Dp and Dp-D(p+4)-brane solutions are constructed in the Penrose
limit of the linear-dilaton geometry. The classical solutions are shown to
break all space-time supersymmetries. In the worldsheet description, the branes
preserve as many supersymmetries as D-branes in flat space. It is shown that
these supersymmetries do not have zero modes on the worldsheet and hence do not
admit local space-time realizations. This indicates that, unlike the
perturbative spectrum, the D-brane spectrum of strings in the linear-dilaton
pp-wave is not similar to the flat space case.
