One of the problems from which the conclusion is not yet obtained is the putative existence of a liquid-liquid phase transition (LLT) in the supercooled regime of a single component system. The main liquid of interest evoked is always water, the properties of which could be engendered by this type of transition and the localization of a 2nd critical point in the phase diagram. Several conflicting interpretations of the nature of the 2 liquid phases have been proposed with, so far, no resolution of the issue, since no experimental evidence could support it. Recently, the possibility of observing such LLT was suggested in two molecular glassforming systems: the triphenylphosphite (TPP) and water-glycerol mixtures at isocomposition (Tanaka, NatMat 2012). Here we propose to explore one of the possible interpretations consisting in a spinodal decomposition (SD) and a nucleation and growth process (NG). The local structure of water within the mixtures during the two processes will be analyzed thanks to the use of polarization analysis on D7; and the evidence of a critical nucleus (case of NG) or its absence in the case of spontaneous SD will be measured by SANS on D22 for both systems.