In this paper wr study T-duality for open strings ending on branes with non
-zero B-field on them from the point of view of canonical transformations.
For the particular case of type Ii strings on the two torus we show that th
e Sl(2,Z)(N) transformations can be understood as a sub-class of canonical
transformations on the open strings in the B-field background. (C) 2000 Pub
lished by Elsevier Science B.V. All rights reserved.