Abstract: Firstly, using extrapolation method of one-sided weights, we established the boundedness of multilinear commutators generated by singular integral
and fractional integral  with function in BMO on weighted Lebesgue spaces. Secondly,  on this basis, we further studied the weighted boundedness of this kind of  commutators of one-sided oscillatory integrals on one-sided  Morrey spaces.

Key words: one-sided oscillatory integral, multilinear commutator, one-sided Morrey space, one-sided weight