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We discuss the nature of the slow relaxation processes in glass-forming eutectic melts right after melting. For specific, we focus on the binary metallic melt Al--Y, which in addition to the slow relaxation shows unusual non-monotonic dynamics. We argue this slow dynamics is an result of non-linearity of diffusion processes in initially non-homogenous sample, and the nature of slow relaxation processes in eutectic melts after melting is similar to the nature of spinodal decomposition, when reason for the slowdown is the thermodynamic instability. To support this assertion we considered the model with combined Gibbs potential of the Al-Y liquid solution, in which the presence of the stoichiometric phase remains is taken into account. We show that in this system the instability mathematically described by the Cahn--Hilliard type equation can develop, and that fluctuation accounting in the considered model allows qualitatively describe the non-monotonic relaxation observed in the Al-based nonequilibrium melts., Comment: 6 figures