The copying of holograms by constructing Gabor type holograms from the originals is discussed mathematically. The analysis is based on plane wave expansions, and the paraxial approximation is not used. Two sets of double images of the original scene appear in the reconstruction process with the copy hologram when emulsion thickness is not important. The separation of the double images is equal to twice the separation of the two photographic emulsions during the copying process. The importance of the extra images is discussed and ways to eliminate them are described. Double images are not produced by copies of wide angle holograms with interference fringe spacing that is small compared to the emulsion thickness.