Abstract: The three-dimensional unsteady second-order non-homogeneous differential equation has been derived by superposition of a small disturbance on a given steady three-dimensional flow. Based on the assumption of high Mach numbers this second-order equation for unsteady flow reduces to a form analogous to that for steady flow. This makes it possible to solve the equation by methods used in the second-order theory for steady flows. In the course of solution the flows are constrained and corrected according to the PLK method, and singularities are thus eliminated. The crucial point in this procedure is to find the correct particular solutions. Two particular solutions are used. One is the approximate three-dimensional particular solution. The other is obtained under the assumption of local two-dimensionality. In addition, the uniform particular solution is given, from which the uniform second-order solutions may be obtained. Then, we have treated the unsteady problem for delta wings with low aspect ratio and supersonic leading edges. The Mach number range for application of the present theory is from supersonic to low hypersonic values with reduced frequencies up to near unity. The theoretical results derived in this work can be used to calculate the unsteady aerodynamic characteristics of wings having arbitrary airfoil sections.As experimental information for similar conditions is not yet available, we can only compare our results with those of Liu D. D. . For this reason, only the derivation for a flat delta wing oscillating at low frequencies has been carried out and an analytical expression is obtained for the first order expansion of the unsteady velocity potential. In the range of Mach numbers 4 to 8, our results are in agreement with those of Lui D. D. .It is also shown that under conditions of three-dimensional thin wings the second-order theory is valid up to Mδ=1.0, while according to application of the second-order theory to bodies of revolution by Van Dyke, the useful upper limit of M5 is only 0.7. Hence, with Mδ=0.7-1 .0, the principal non-linear effects can be calculated by our second-order theory, while for thin wings the third-order terms connected with heat transfer and entropy change can be ignored.