Properties of alkali metal hydrogensulphate MeHSO4 (Me = Cs, Rb, K) in (1 - x)MeHSO4-xA (A = Al2O3, TiO2, SiO2; x = 0-0.9) nanocomposite solid electrolytes were studied by X-ray powder diffraction, differential scanning calorimetry methods and conductivity measurements. The conductivity of the composites was shown to exceed that of the individual salts by more than 1-3.5 orders of magnitude and to depend on composition. The conductivity and thermal stability of (1 - x)CsHSO4-xA composites increase in the order Al2O3 < TiO2 < SiO2. The properties of composites (1 - x)MeHSO4-xSiO(2) depend markedly on the grain and pore size of silica. The optimum SiO2 pore size was in the range 35-100 Angstrom. where the highest composite conductivity was observed. For these composites, the enthalpies of CsHSO4 and RbHSO4 phase transitions and melting decreased considerably and the thermal stability increased. The ionic component became amorphous. Analysis of calorimetric data indicated the presence of two crystalline phases with different temperatures of phase transition and melting in the composites with silica of pore size 170 Angstrom. The MeHSO4 state changed slightly when the SiO2 pore size was 1000 Angstrom. In the systems with pore size of 14 Angstrom, both crystalline and amorphous salts were observed.