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The present paper investigates the bulk metallic,lass formation ill Cu-Zr-Al and Cu-Zr-Ti ternary systems by using the cluster line criterion. The binary basic Clusters are first selected for constructing cluster lines. Three cluster selection rules are proposed: topologically dense packing, chemical short-range order and composition distance to deep eutectics. Three Cu-Zr clusters Cu8Zr5, Cu6Zr5 and Cu5Zr6 are selected according to the three rules. The bulk metallic glass-forming ranges in these two systems are determined. The thermal characteristic parameters of the Cu-Zr-Al BMGs on every composition line increase with increasing Al content and decrease with increasing Ti content in the Cu-Zr-Ti glass-forming range. The optimum bulk amorphous compositions in the Cu-Zr-Al system are Cu58.1Zr35.9Al6 and Cu39.7Zr47.1Al13.2, respectively, located in Cu8Zr5-Al and Cu5Zr6-Al Cluster lines. In the Cu-Zi-Ti system, the Cu64Zr28.5Ti7.5 composition with the largest T-g/T-l is located in Cu9Zr4-Ti cluster line and the Cu57.6Zr32.4Ti10 composition with the largest glass-forming ability is located in Cu64Zr36-Ti line. (c) 2006 Elsevier Ltd. All rights reserved.