Inelastic deformation of a defect-free lattice emerges when the elastic stiffness coefficients for the whole system, or the global (system) stability, loses the positive definiteness. Disordered crystals, however, show inhomogeneous deformation from the very begining and the coefficients never becomes negative even at the onset of inelastic deformation. The present study is the first report on the relationships between the global and local (atomistic) stabilities in such disordered systems. First, many static calculations are performed for the global stability of nickel nano-polycrystals by changing cell size, ratio of grain boundaries and grain orientations in a cubic periodic cell. The global stability increases by grain subdivision of 2×2×2, then decreases with the number of grains. This is because of hardening by random crystal orientation and softening by increase of grain boundaries. Then the polycrystals with the cell size of 30a×30a×30a (a is the lattice parameter of nickel) are relaxed by means of molecular dynamics simulation to evaluate the local stability before loading. Contrary to the global stability, the average of local stability monotonically decreases with the number of grains, from that of a perfect lattice to amorphous. Finally, we have performed tensile simulations and investigated the change in yield stress, global and local stabilities.