The present study reveals the role of Nb and Ni minor addition on the nanomechanical properties and nanostructure of ZrCuAl bulk metallic glass (BMG). For this purpose, atomic force microscopy (AFM) was used to evaluate the viscoelastic response of the BMG surface at the nanoscale, while the nanoindentation technique was applied to show the mechanism of plastic deformation. The results indicated that minor Nb addition decreased the relaxation of enthalpy accompanied by the weakening of structural heterogeneity. On the other hand, Ni addition improved the stored energy of the material and intensified the distribution of loosely packed regions in the microstructure. Moreover, the mechanical test unveiled that Ni addition enhanced the viscoelastic response; however, it came at the expense of creep resistance. The evaluation of the magnitude of the derivative in the nanoindentation test also demonstrated that the Ni-added sample exhibited a multiple shear-band mode for plastic deformation.