  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.
