Abstract: In ihis paper.an instability problem of an unsteady oscillationo flow is studied.In particultar,the phase.function of the disturbance wave.system is soived by using the charocteristic theory of partial differential equation and an expansion of Orysommerfeid eigenvalue problem.instead of using the disturbance model which is given previously The.flow considered is a combination of plane Poiseuille.flow with aflow oscillating periodically and its instability is found for a special initial value of a developing wave due to continuous oscillationg source.

Key words: through flow, Charpsits method, phase function, Pfaffian equation, instability