  In this paper, we present several gravitational wave solutions in AdS_5 X S^5
string backgrounds, as well as in AdS_7 X S^4 and AdS_4 X S^7 backgrounds in
M-theory, generalizing the results of hep-th/0403253 by one of the authors. In
each case, we present the general form of such solutions and give explicit
examples, preserving certain amount of supersymmetry, by taking limits on known
BPS D3 and M2, M5-brane solutions in pp-wave backgrounds. A key feature of our
examples is the possibility of a wider variety of wave profiles, than in pure
gravity and string/M-theory examples known earlier, coming from the presence of
various p-form field strengths appearing in the gravitational wave structure.
