The Debye-Huckel theory has been extended to allow for arbitrary concentration dependence of the electrolyte solution static permittivity. The theory follows the lines advanced by Erich Hiickel (Huckel, E. Physt Z. 1925, 26, 93) but gives rise to more general and lucid results. New theoretical expressions have been obtained for the excess free energy of solution, activity coefficient of water and mean ionic activity coefficient. The thermodynamic functions contain two ternis representing interionic interactions and ion water (solvation) interactions. The theory has been applied to calculate the activity coefficients of components in the aqueous solutions of alkali metal chlorides from LiCl to CsCl at ambient conditions making use of permittivities taken from experimental dielectric relaxation studies. Calculations without parameter adjustment have demonstrated a 8emiquatititative agreement with experimental data, reproducing both the nonmonotonic concentration dependence of the activity coefficients and the ordering of activity coefficients for the salts with different cations. A good agreement with experimental data is obtained for the aqueous solutions of LiCl in the concentration range up to 10 mol/kg, The nonmonotonic concentration dependence of activity coefficients is explained as a result of a balance between the effect of interionic interactions and the solvation contribution which appears quite naturally in the framework of the Debye Hiickel approach after incorporation of variable permittivity of solution.