Studies are carried out of morphology, crystal structure, chemical content, thermal and transport properties of Li2SO4-Al2O3 composites prepared in two different ways : by thermal decomposition of the precursor Li2SO4.2Al(OH)(3).mH(2)O at 400 degrees C or by using conventional mixing. It is shown that, whatever the preparation technique, if grain size of alumina in composites is small enough (of order of tens nanometers) then after prolonged heating the heterogeneous system Li2SO4-Al2O3 reaches the metastable thermodynamic state - a nanocomposite in which lithium sulphate is in an unusual epitaxial state. The stabilization of this state is caused by a strong interface interaction that is leading to the formation of the intermediate thin layer of lithium aluminate which "glues" Li2SO4 and Al2O3 phases providing the contact. The phase transition temperature of Li2SO4 in composites is 100 degrees lower than in the pure salt. Ionic conductivity of Li2SO4 in the composites smoothly changes at the phase transition, activation energies being 0.40+/-0.05 and 0.66+/-0.01 eV for T>470 degrees C and T<280 degrees C, respectively. The value of the charge carrier concentration in the nanocomposites estimated from the frequency dependent conductivity turned out to be comparable with that in glasses and superionic conductors.