The kinematic viscosity of Cu-Ni melts with nickel contents of 10, 20, 30, 40, 50, 60, 70, 80, and 90 at % is measured. Kinematic viscosity is measured using the damped torsional vibrations of a crucible with a melt in the mode of sample cooling. The measuring results are discussed within the theory of absolute reaction rates. The temperatures at which the viscous flow characteristics (and thus the structural state of the melt) change are determined by analyzing the temperature dependences of kinematic viscosity. The patterns of the liquid-liquid transition in metal alloys of the Cu-Ni system that form a continuous series of solid solutions during crystallization are analyzed.