We examined the thermal stability, glass-forming ability (GFA) and mechanical properties of Mg-Y-Zn(-Cu) base alloys produced by melt-spinning and copper mold casting methods. The glass-forming ability of Mg-Y-Zn ternary glassy alloys was not high enough to form a bulk glassy alloy by the copper mold casting method. The Cu addition to form the Mg₆₅Y₁₀Zn_25−xCu_x (x=0 to 25 at%) quaternary alloys resulted in a significant increase in GFA and thermal stability of the amorphous phase. The compressive fracture strength, Young’s modulus and ductility of the Mg₆₅Y₁₀Zn₅Cu₂₀ bulk glassy alloy are higher than those of Mg₆₅Y₁₀Cu₂₅ bulk glassy alloy, although the GFA of the Mg₆₅Y₁₀Zn₅Cu₂₀ alloy is slightly lower than that of the Mg₆₅Y₁₀Cu₂₅ alloy.