A novel marching-on-time (MOT) based scheme for solving a time domain integral equation (TDIE) was discussed. It was observed that the scheme was pertinent to the analysis of plane wave scattering from nonplanar doubly periodic structures with unit cells comprising perfect electrically conducting (PEC) elements and inhomogeneous dielectric volumes. This scheme aimed at rendering the solver applicable to the nonplanar structures. The resulted scheme was applied without any difficulty to nonplanar doubly periodic structures comprising PEC and sculptured dielectric substrates.