A new model is presented that explains reaction time fluctuations in prolonged work tasks. The model extends the so-called Poisson-Erlang model and can account for long-term trend effects in the reaction time curve. The model is consistent with Spearman's hypothesis that inhibition increases during work and decreases during rest. Predictions concerning the longterm trend were tested against data from the Bourdon-Vos cancellation test. The long-term trend in the mean and in the variance was perfectly described by the model. A goodness-of-fit test comparing frequency distributions of observed reaction and simulated reaction times was also supported by the model. Index terms: concentration, continuous work, distraction, inhibition, prolonged work, reaction time, response time.