Growth phenomena are often nonlinear and may contain spurts, characterized by a local increase in the rate of growth. Because measurement error and noise may produce apparent spurts, it is important to identify systematic and reliable spurts. We describe a system, automatic maxima detection (AMD), for statistically identifying significant spurts and computing (1) point of maximal velocity, when the spurt was most intense; (2) start, when the spurt started; (3) amplitude, the intensity of the spurt; and (4) duration, the length of the spurt. We also introduce a software implementation of AMD in MATLAB. In growth of height data, AMD showed a reliable pubertal growth spurt for most children and a reliable prepubertal spurt for some children. In simulated growth of vocabulary, AMD showed a large global spurt and several minispurts. In real vocabulary growth, AMD showed a few spurts. Advantages of AMD include improvements in objectivity, automaticity, quantification, and comprehensiveness.