  It is well known that space-time coordinates and corresponding Dp-brane
world-volume become non-commutative, if open string ends on Dp-brane with
Neveu-Schwarz background field $B_{\mu \nu}$. In this paper we extend these
considerations including the dilaton field $\Phi$, linear in coordinates
$x^\mu$. In that case the conformal part of the world-sheet metric appears as
new non-commutative variable and the coordinate in direction orthogonal to the
hyper plane $\Phi = const$, becomes commutative.
