Based upon classical hypotheses about accumulating mental fatigue and distraction and its effect on response times, put forward in late 19th and early 20th century papers, a mathematical model is proposed for response times on tests of speed and concentration. The model assumes the random occurrence of very short distractions during information processing. It explains fluctuation and the increasing trend in response times on successive equivalent task units and leads to some simple diagnostic RT measures of speed and concentration as alternatives to the mean RT. A review is given of several experimental applications of the model, with subjects with and without concentration problems, using cancellation and digit addition tasks. The results demonstrate the potential usefulness of the model and the diagnostic measures derived from it. As predicted by the model, prolonged task performance yields an increasing trend in RT mean and variance that can be strongly reduced by giving very short resting periods very frequently, and to a lesser extent also by task alternation, but not by simply motivating the subjects to concentrate. Some practical implications for the administration and scoring of tests of speed and concentration are discussed, as well as limitations of the present results and the complementary relation of our approach to popular ones such as "stage analysis."