The antiphase boundary in a superlattice has been defined as the boundary between two neighboring zones which are out ofsphase with each other. This difference in phase is usually represented by a translation vector. In long-period superlattices, however, antiphase boundaries of the above mentioned type occur with regular spacings, thereby introducing another element of order which shows up as satellite peaks in the diffraction pattern. A second kind of antiphase boundaries may be defined in a one-dimensional long-period superlattice as the boundary between two neighboring zones which have different directions of repetition of the antiphase boundaries of the first kind. A theory of X-ray diffraction to obtain the size of the domains of the second kind in a one-dimensional long-period superlattice has been developed. An application of this theory to the ordered alloy Ag3Mg, known to have a one-dimensional long-period superlattice, is described and the results of the X-ray measurements are compared with those obtained by transmission electron microscopy.