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The relaxation behavior of Ca60Mg20Zn20, Ca60Mg20Cu20, Ca65Mg15Zn20, Ca50Mg20Cu30, and Ca55Mg18Zn11Cu16 bulk metallic glasses was determined in the glass transition region using differential scanning calorimetry (DSC) with heating rates from 1 to 160 K/min. The activation enthalpy of structural relaxation and the fragility index m were found to be smaller in the glassy state (onset of the glass transition) than in the supercooled liquid state (end of glass transition). The Ca-based glass-forming liquids showed strong behavior of the relaxation time, with the fragility indexes m in the range of 33 to 40. The strong liquid behavior implies sluggish kinetics of crystallization in the supercooled liquid region and explains the very good glass-forming ability (GFA) of these alloys. The critical cooling rate for amorphization Rc of the Ca-based bulk metallic glasses was estimated to be in the range of 0.3 to 10 K/s, which is similar to Rc values for the best Pd- and Zr-based metallic glass-forming alloys discovered so far.