1. A study has been carried out on the steady-state kinetics followed by the alkaline phosphatase from Escherichia coli at different pH, temperatures, ionic strengths, phosphate concentrations and in the presence of the effectors such as Tris, NH4+--NH3 and CH3OH; p-nitrophenyl phosphate was used as substrate. 2. Contrary to what has generally been accepted, in most cases the enzyme follows non-Michaelian kinetics for a wide substrate concentration range, giving concave-down Lineweaver-Burk plots. Only at high phosphate concentrations (5 . 10(-3) M) and at high ionic strengths (2.0 M) is a linear Lineweaver-Burk plot obtained (Michaelian kinetics). 3. In order to analyse the kind of kinetics obtained, a non-linear regression fitting method was used to obtain rate vs substrate concentration equations as polynomial quotients of minimum degree with positive coefficients. 4. Most of the data obtained follows 2:2 degree type equations. 5. These results tend to suggest an idea of cooperativity rather than one of independence between the sites of the dimeric enzyme. A model is discussed for cooperativity between the sites with a wide concentration range giving concave-down Lineweaver-Burk plots.