An electrolyte for rechargeable batteries with a negative electrode of lithium or lithium containing alloys comprising: one or several non-aqueous organic solvents, one or several lithium salts and one or several additives increasing the cycle life of the lithium electrode. The electrolyte solution may comprise one or several solvents selected from the group comprising: tetrahydrofurane, 2-methyltetrahydrofurane, dimethylcarbonate, diethylcarbonate, ethylmethylcarbonate, methylpropylcarbonate, methylpropylpropyonate, ethylpropylpropyonate, methylacetate, ethylacetate, propylacetate, dimetoxyethane, 1,3-dioxalane, diglyme (2-methoxyethil ether), tetraglyme, ethylenecarbonate, propylencarbonate, γ-butyrolactone, and sulfolane. The electrolyte solution may further comprise at least one salt or several salts selected from the group consisting of lithium hexafluorophosphate (LiPF6), lithium hexafluoroarsenate (LiAsF6), lithium perchlorate (LiClO4), lithium sulfonylimid trifluoromethane (LiN(CF3SO2)2)) and lithium trifluorosulfonate (CF3SO3Li) or other lithium salts or salts of another alkali metal or a mixture thereof. Also disclosed is an electrochemical cell or battery with an anode of metallic lithium or a lithium-containing alloy, and such an electrolyte.