Objects that temporally vary slowly can be superresolved by the use of two synchronized moving masks such as pinholes or gratings. This approach to superresolution allows one to exceed Abbe's limit of resolution. Moreover, under coherent illumination, superresolution requires a certain approximation based on the time averaging of intensity rather than of field distribution. When extensive digital postprocessing can be incorporated into the optical system, a detector array and some postprocessing algorithms can replace the grating that is responsible for information decoding. In this way, no approximation is needed and the synchronization that is necessary when two gratings are used is simplified. Furthermore, we present two novel approaches for overcoming distortions when extensive digital postprocessing cannot be incorporated into the optical system. In the first approach, one of the gratings, in the input or at the output plane, is shifted at half the velocity of the other. In the second approach, various spectral regions are transmitted through the system's aperture to facilitate postprocessing. Experimental results are provided to demonstrate the properties of the proposed methods.