The anomal temperature dependences of the transverse NMR-relaxation time T2 of solvent molecules water and DMSO in agarose gels have been obtained being qualitatively explained in the framework of the three-phase model with the molecular exchange between phases. Acceleration of the transverse magnetic relaxation of solvent molecules in agarose gels is explained by the presence of few fast-relaxing molecules incorporated into the network points of a gel. The values of the activation energy of molecular exchange and of the content of molecules with short T2 time are numerically evaluated