Low-dimensional quantum-well and nanoisland heterostructures formed in the InSb/AlAs system by molecular-beam epitaxy are studied by transmission electron microscopy and steady-state photoluminescence spectroscopy. The structures are grown under conditions of alternate In and Sb deposition (the socalled atomic-layer epitaxy mode) and the simultaneous deposition of materials (the traditional molecularbeam epitaxy mode). In both modes of growth, at a nominal amount of the deposited material in a single layer, large-sized (200 nm–1 μm) imperfect islands arranged on the InxAl1 – xSbyAs1–y quantum-well layer are formed. In the heterostructures grown under conditions of atomic layer epitaxy, the islands are surrounded by ring-shaped arrays of much smaller (~10 nm), coherently strained islands consisting of the InxAl1 – xSbyAs1 – y alloy as well. The composition of the alloy is defined by the intermixing of Group-V materials in the stage of InSb deposition and by the intermixing of materials because of the segregation of In and Sb atoms during overgrowth of the InSb layer by an AlAs layer.