  We derive the commutation relations for open-string coordinates on D-branes
in non-geometric background spaces. Starting from D0-branes on a
three-dimensional torus with H-flux, we show that open strings with end points
on D3-branes in a three-dimensional R-flux background exhibit a non-associative
phase-space algebra, which is similar to the non-associative R-flux algebra of
closed strings. Therefore, the effective open-string gauge theory on the
D3-branes is expected to be a non-associative gauge theory. We also point out
differences between the non-associative phase space structure of open and
closed strings in non-geometric backgrounds, which are related to the different
structure of the world-sheet commutators of open and closed strings.
