  We construct a calculational scheme for handling the matrix ordering problems
connected with the appearance of D-brane positions taking values in the same
Lie algebra as the nonabelian gauge field living on the D-brane. The formalism
is based on the use of an one-dimensional auxiliary field living on the
boundary of the string world sheet and taking care of the order of the matrix
valued fields. The resulting system of equations of motion for both the gauge
field and the D-brane position is derived in lowest order of the $\alpha'$
-expansion.
