We have found a new type ordering structure in materials containing Indium. Generally conventional natural superlattice (NSL) stacks toward to {111}. However, the periodical structure in question stacks along the [001] direction, sometimes parallel to the substrate. We have studied the structure in detail as seen in InAlAs-bulk layers on a vicinal (001) InP substrate. We investigated the structure using a transmission electron microscope and a high-resolution X-ray diffraction method, and confirmed the structure stacks along [001] direction with a pitch three times that of the InP lattice constant. We found a similar structure in InAlGaP-bulk layers on a (100) GaAs substrate 10degrees tilted toward the (011) direction. The mechanisms have not been clarified yet, however, we consider that atomic steps on the epitaxial surface could be related. (C) 2004 Elsevier B.V. All rights reserved.