Some practical criteria are suggested for establishing the precision, reproducibility, validity and specificity of quantitative histochemical techniques used for assaying the activities of enzymes in single cells and tissue sections. To be valid, a technique should ideally pass 12 tests. Principally these involve proving that the mean absorbance or fluorescence of the specific final reaction product (FRP) is related to section thickness, incubation time, substrate concentration and the concentration of enzyme in situ. However, the formation of appreciable amounts of non-specific FRP may interfere in the determination of the true enzyme activity. This and other difficulties are illustrated with data obtained from an investigation of Meijer's semipermeable membrane technique for assaying acid phosphatase in unfixed sections of muscle.