  The kappa-invariant and supersymmetric actions of D1 and D5-branes in AdS_3 x
S^3 are investigated, as well as the action of a D5-brane in an AdS_5 x S^5
background. The action of a D5-brane lying totally in an AdS_3 x S^3 background
is found. Some progress was made towards finding the action for the D5-brane
free to move in the whole AdS_3 x S^3 x T^4 space, however the supersymmetric
action found here is not kappa-invariant and the reasons the method used did
not find a kappa-invariant solution are discussed.
