  We present classical solutions for a D5 and NS5-branes in a pp-wave
background. The worldvolume coordinates for these branes lie along a six
dimensional pp-wave configuration obtained from $AdS_3 \times S_3$ in a Penrose
limit. One in addition has nontrivial R-R 3-form field strength as well as a
dilaton background. Classical solutions for Dp-branes (p> 5), as well as their
bound states, are then generated in both IIA and IIB string theories by using
T-duality symmetries. We also briefly discuss the construction of Dp-branes in
pp-wave backgrounds, obtained from string theories on $AdS_m\times S^m$.
Finally, the construction of the above D5-brane solution is presented from the
point of view of the Green-Schwarz worldsheet string theory and its low lying
spectrum is discussed.
