We show that the tendency towards microphase separation in microemulsions can lead to the formation of a glassy state after sufficiently strong correlations between polar and hydrophobic regions have been established. Glassiness is predicted to occur above a critical volume fraction of surfactant molecules, which is determined by the length of the amphiphilic molecules. Our results are obtained by solving the dynamical equations for the correlation functions of the system and by using a replica approach. (C) 2002 Published by Elsevier Science B.V.