A method for determining initial velocities of enzymatic reactions at very low substrate concentrations is presented. It is based on the continuous perfusion of substrate-containing media through the enzyme, previously deposited as a thin layer on a solid support. An analytical rationalization of the dependence of the enzymatic activity upon the substrate supply and the flow rate was developed (substrate supply (mumol/min) = flow rate (ml/min) x inflowing substrate concentration (mumol/ml). This paper shows that a straight line should be expected from a double-reciprocal plot of the velocity of the enzymatic reaction and flow rate. The reciprocal of the ordinate at the origin is the strict initial velocity for a given, constant, and very low substrate concentration, since substrate consumption and product accumulation tend to zero. Results obtained with two different sarcoplasmic reticulum (Ca2+ + Mg2+)-ATPase preparations agree with the theoretical predictions. The method enabled the use of ATP concentrations in the range of 10(-8) M; it required neither an ATP-regenerating system nor the dilution of the enzyme protein, and it presented no limitations for the reaction time. Both ATPase preparations showed two apparent Km values for the substrate in the submicromolar and micromolar ranges: 0.25-12.0 microM for the purified ATPase, and 0.17-1.65 microM for the microsomal ATPase.