The process forms a phosphate coating on a steel strip or sheet having a galvanized or alloy galvanized side and a steel side so that the phosphate coating is only present on the galvanized or alloy galvanized side. This process includes contacting the galvanized or alloy galvanized side of the steel strip or sheet with a phosphatizing solution for 4 to 20 seconds at a temperature of from 45.degree. C. to 80.degree. C. The phosphatizing solution has an S value of from 0.08 to 0.30 and contains 0.5 to 5 g/l zinc, 3 to 20 g/l P.sub.2 O.sub.5, 0.020 to 0.2 g/l nitrite, 3 to 30 g/l nitrate and 0.2 to 2.5 g/l complexing agent for iron. Chelate forming substances, such as tartaric acid, citric acid, ethylenediamine-tetraacetic acid, nitrilotriacetic acid and/or oxalic acid, may be used as the complexing agent for iron. The phosphatizing solutions may also contain other bivalent cations, particularly manganese and/or nickel cations.