The temperature and time dependences of the viscosity of liquid ternary alloys Al87Ni8Y5, Al86Ni8La6, Al86Ni8Ce6, Al86Ni6Co8, Al86Ni10Co4 and binary melts Al90(Y/Ni/Co)10 have been studied after different temperature-time treatment of the melt. It is shown that long-time relaxations in the Al-TM-R melts occur only after the phase transition “crystal-liquid” due to the melt transition from the non-equilibrium to equilibrium state. The non-equilibrium state of the melt appears due to inheriting non-equilibrium atomic groups during melting; the atomic groups have ordering characteristic of chemical compounds of the AlxRу type present in solid-state alloys.