The crystal structures of highly-ordered Mg-Zn-Y long-period stacking-ordered (LPSO) phases with the 18R-, 14H- and 10H-type stacking sequences, which are constructed by stacking structural blocks composed of six, seven and five close-packed atomic layers, respectively, have been investigated by atomic-resolution scanning transmission electron microscopy (STEM) and transmission electron microscopy. The in-plane order characterized by the periodic arrangement of Zn6Y8 atomic clusters on the lattice points of a 2 root 3a(mg) x 2 root 3a(mg) two-dimensional primitive hexagonal lattice (a(mg): the lattice constant of Mg) is developed in the central four consecutive atomic layers in each of the structural blocks for the 18R-, 14H- and 10H-type Mg-Zn-Y LPSO phases. The random occupation of the central site of each Zn6Y8 atomic cluster with Mg, Zn, Y or vacancy is suggested through the analysis of the ultra-high resolution annular-bright field STEM images. The space groups of the most stable polytypes of the 18R-, 14H- and 10H-type Mg-Zn-Y LPSO phases at 500 degrees C are determined to be C2/c, P6(3)22 and Cmce, respectively. (C) 2015 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.