The processes of melting and crystallization of Ni nanoclusters with a diameter to 3.6 nm have been studied by the molecular-dynamics method based on tight-binding potentials. The effect of the particle size on the stability of the structural modifications obtained has been investigated. The dependence of the process of the cluster-structure formation on the conditions of cooling from the liquid state has been noted. Upon slow crystallization, an fcc structure was mainly formed, whereas upon rapid cooling an icosahedral phase was formed in the majority of cases. Thus, the simulation performed indicates the possibility of some control of the structure formation of Ni clusters upon crystallization.