We examine non-abelian duality transformations in the open string case
. After gauging the isometries of the target space and developing the
general formalism, we study in detail the duals of target spaces with
SO(N) isometries which, for the SO(2) case, reduces to the known abeli
an T-duals. We apply the formalism to electrically and magnetically ch
arged 4D black hole solutions and, as in the abelian case, dual coordi
nates satisfy Dirichlet conditions.