The time dependent turbulent boundary-layer equations are integrated numerically with a two-layer eddy viscosity model (Cebeci-Smith formulation), for transient or oscillatory outer flows. Comparisons with previous theoretical results indicate that the present method is at least as good as the others. Extensive comparisons with experimental data also are attempted for the first time. It appears that in a certain range of frequencies the agreement is satisfactory. Further, some characteristic quantities, like the mean velocity profile or the wall shear phase angle, are predicted accurately but other properties, like the averaged fluctuations of the velocity, indicate some discrepancies. The present method also is capable of integrating past the point of zero skin friction and into regions of partially reversed flow. The phenomenon of separation in unsteady flow also is investigated.