[en] We use first-principles density functional theory total energy calculations based on pseudo-potentials and plane-wave basis to assess stability of the periodic structures with different stacking sequences in Mg-Zn-Y alloys. For pure Mg, we find that the 6-layer (6l) structure with the ABACAB stacking is most stable after the lowest energy hcp (2l) structure with ABAB stacking. Addition of 2 at.% Y leads to stabilization of the structure to 6l sequence whereas the addition of 2 at.% Zn makes the 6l energetically comparable to that of the hcp. Stacking fault (SF) on the basal plane of 6l structure is higher in energy than that of the hcp 2l Mg, which further increases upon Y doping and decreases significantly with Zn doping. SF energy surface for the prismatic slip indicates activation of non-basal slip in alloys with a 6l structure. Charge density analysis shows that the 2l and 6l structures are electronically similar which might be a cause for better stability of 6l structure over a 4l sequence or other periodic structures. Thus, in an Mg-Zn-Y alloy, Y stabilizes the long periodicity, while its mechanical properties are further improved due to Zn doping