  Ascertainment of the nature of the slow relaxation processes observed after
melting in glass-forming eutectic melts is the subject of this work. We claim
that the diffusion processes nonlinearity in heterogeneous melt with inclusions
of refractory stoichiometry is the origin of this phenomenon. The cause for
this nonlinearity is the thermodynamic instability similar to one taking place
at spinodal decomposition, and indispensable condition is the initially
non-homogenous. For confirmation of our devotes, we consider the model of
liquid solution of a binary system, which evolution described by the
Cahn-Hilliard equation with combined Gibbs potential assuming the presence of
remains after melting stoichiometric phase. Exemplified by the Al-Y and Al-Yb
alloys, using Gibbs potentials from a standard database we show that subject to
initial heterogeneity in these systems the instability can develop leading to
the slow relaxation processes, and determine the regions of this instability in
the phase diagrams.
