Special role in computer simulations of supercooled liquid and glasses is played by few general models representing certain classes of real glass-forming systems. Recently, it was shown that one of the most widely used model glassformers -Kob-Andersen binary Lennard-Jones mixture -crystalizes in quite lengthy molecular dynamics simulations and, moreover, it is in fact a very poor glassformer at large system sizes. Thus, our understanding of crystallization stability of model glassformers is far from complete due to the fact that relatively small system sizes and short timescales have been considered so far. Here we address this issue for two embedded atom models intensively used last years in numerical studies of Cu-Zr-(Al) bulk metallic glasses. We consider Cu64.5Zr35.5 and Cu46Zr46Al8 alloys as those having high glass-forming ability. Exploring their structural evolution at continuous cooling and isothermal annealing, we observe that both systems nucleate in sufficiently lengthy simulations, though Cu46Zr46Al8 demonstrate order of magnitude higher critical nucleation time. Moreover, Cu64.5Zr35.5 is actually unstable to crystallization for large system sizes (N > 20, 000). Both systems crystallize with the formation of tetrahedrally close packed Laves phases of different types. We reveal that structure of both systems in liquid and glassy state contains comparable amount of polytetrahedral clusters. We argue that nucleation instability of simulated Cu64.5Zr35.5 alloy is due to the fact that its composition is very close to that for stable Cu2Zr compound with C15 Laves phase structure. arXiv:1809.00198v1 [cond-mat.mtrl-sci] 1 Sep 2018