Working with pure lipidic systems (giant unilamellar vesicles, 10-150 microm in diameter) as models for biological membranes, we have considered possible structures of the contact area of two adherent membranes by investigating the diffusion of fluorescent lipid analogues from one vesicle to another. Two bilayers in close contact can almost be seen as a lamellar structure in equilibrium. This is the usual configuration of two adherent vesicles, in which the interbilayer distance is estimated to be 3 nm. We have increased the attraction between the membranes by either adding depletion forces or by using a trick, inspired from the interaction between nucleic bases in nucleosides (herein adenosine and thymidine). The nucleosides were attached to the polar head of amphiphilic molecules that behave like phospholipids and were incorporated in the model membrane. The extra attraction between two membranes, resulting from base pairing, strongly decreased the interbilayer distance down to about 1 nm. This change of the water content induced lipid rearrangements, which could also be viewed in terms of a phase transition at low water content. These rearrangements were not observed in the case of depletion forces. We conclude that the introduction of an additional attractive force in the system modifies the equilibrium state, leading to a drastic change in the membrane behavior, which will tentatively be related to hemifusion.