Statistics for The oscillatory flow of a homogeneous, conducting, viscous fluid in a channel of varying cross section is considered. The solutions for large Womersley number ? are obtained by the method of matched asymptotic expansions, supplementing the earlier work of Ramachandra Rao and Deshikachar. It is observed that the magnetic field provides an appropriate length scale necessary for matching the solutions and thus resolves the difficulty arising in the corresponding non-magnetic case. © 1989.