An unsteady flow theory is presented for studying the flowfield in the compression side of an oscillating flat delta wing with attached shock waves. Regular perturbation methods are used to analyze the in-phase and outof-phase flow components for small amplitudes and reduced frequencies. In particular, the out-of-phase flow is found to be "quasiconical," thus a pressure formulation can be realized. In the outboard region, where the crossflow is supersonic, exact solutions are found representing parallel surfaces of isobars. In the central region where the crossflow is subsonic, the problem is reduced to that of an ordinary-differential equation by a spanwise integration technique. Closed-form solutions are obtained for all cases. Numerical examples are presented to exhibit the dependence of the damping derivatives on several flow and geometrical parameters. Neutral damping boundaries are also given. It is found that the damping derivatives are generally less sensitive to the sweepback-angle and the freestream Mach number variations than to the mean-incidence variations, except near the shock detachment. Critical assessments, improvement schemes and future extensions were also discussed.