The activity of pepsin, the gastric protease, is generally considered to be negligible for pH ≥ 4, based on results obtained with few purified globular proteins. The present study aimed at studying the activity of porcine pepsin on egg white proteins (EWP) and casein micelles (CA) over a broad range of pH (from 1 to 7) at short (3 min) and long (2 h) digestion times. At short time, results confirmed a tendency for a higher rate of hydrolysis with decreasing pH, but with different pH activity profiles for both substrates. More remarkably, the degree of hydrolysis of CA after 2 h of digestion was constant from pH 1 to pH 5, and was only reduced by half at pH 6. This finding demonstrates that pepsin can hydrolyse caseins from the very beginning of gastric digestion. Interestingly, the shape of the reaction kinetics over 2 h appeared to be rather characteristic of the type of substrate and largely independent on pH. Most hydrolysis profiles could be accurately fitted by a power law, an empirical model that was then successfully applied to the static in vitro gastric proteolysis of 6 other food matrices. Overall, our results support the idea that pepsin activity in weakly acidic conditions (pH ≥ 4) should not always be neglected, in particular for milk caseins, and that pepsin reaction kinetics during static in vitro gastric digestion seem to evolve proportionally to the power of digestion time.