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The angular non-critical phase-matching (A-NCPM) second-harmonic-generation (SHG) properties of RE1_xRE2_1−xCOB (RE1, RE2 = Y, Gd, La, Tm, Sm, and Nd) type mixed crystals including NCPM wavelength and conversion efficiency were detailedly investigated. Theoretical calculations manifest that the A-NCPM SHG scope of these crystals is 0.72~1.42 µm, and in experiments, the A-NCPM SHG waveband of 0.72~1.25 µm has been realized, by changing the ratio of the rare-earth elements RE1 and RE2 in RE1_xRE2_1−xCOB crystals. Comparing to the temperature-dependent A-NCPM SHG of 0.95~1.34 µm in LiB₃O₅ (LBO) crystal, the composition-dependent A-NCPM SHG of 0.72~0.95 µm in RE1_xRE2_1−xCOB type crystals is unique and has special significance for the frequency conversion of Ti:Sapphire lasers. Relationships between the birefringence and radius of rare-earth ion RE³⁺ in RE1_xRE2_1−xCOB mixed crystals were discussed. Aiming for the A-NCPM SHG of 0.72~1.42 µm, we supply a clear, completed, and optimized solution on how to select the compositions of RE1_xRE2_1−xCOB mixed crystals. Under focusing light beam conditions, high efficient A-NCPM SHG for both OPO and Ti:sapphire lasers were realized experimentally by using long Y- and Z-cut RE1_xRE2_1−xCOB crystal samples.