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 details the duals oftarget spaces with SO(N) isometries
which, for the SO(2) case, reduces to the known abelian T-duals. We apply the
formalism to electrically and magnetically charged 4D black hole solutions and,
as in the abelian case, dual coordinates satisfy Dirichlet conditions.Comment: 18 pages, Latex. Some formulas are added. Final version to appear in
Nucl. Phys.