Present invention relates to an anhydrous hair lightening/bleaching composition comprising two alkaline salts. Accordingly, the present invention is on an anhydrous composition for lightening and/or bleaching hair comprising at least one alkalizing agent, at least one guanidine salt, at least one second alkaline salt selected from salts of carbonates, bicarbonates, phosphate and hydrogenphosphates with a cation selected from sodium or potassium and at least one oil liquid at 20°C, wherein the composition is free from ammonia.