Novel long-period hexagonal structures with six and fourteen layered atomic configurations were formed in melt-spun Mg₉₇Ln₂Zn₁ (Ln=Y, Gd and Sm) ternary alloys annealed at 573 K for 1.2-3.6 ks and in an as-spun Mg₉₇Y₂Zn₁ alloy, respectively. The Mg-based alloys containing La or Ce as the Ln element have a mixed structure of hcp Mg and compound phases and no long-period hexagonal structure is formed in the as-spun and annealed states. There is a clear formation tendency of the novel long-period structure to increase with a decrease in the precipitation tendency of the intermetallic compound, an increase in the atomic size ratio of Ln/Mg and an enhancement of the formation tendency of Mg-based reinforced solid solution. The formation of the novel long-period structure is interpreted to result from the necessity of relaxation of strains caused by the reinforced solid solution of Ln and Zn elements into the Mg phase. In addition, the enrichment of Y and Zn elements was observed at the misfit sites of the atomic array in the fourteen layered hexagonal structure of the as-spun Mg₉₇Y₂Zn₁ alloy. The atomic level segregation of Y and Zn elements is also thought to be the origin for the high stability of the long-period structure. The two types of long-period hexagonal structures found in the Mg-Ln-Zn alloys are important as a new mechanism for future development of high-strength Mg-based alloy.