We consider symbolic sequences of copepod behavior, classified as “break” and “slow swimming” states. Successive residence times for each state have been recorded for 327 symbolic times series obtained from 52 different trajectories. We performed a symbolic dynamics analysis of the succession of states and showed that the probability densities of the duration of each state obey power-laws for large times. We analyzed the transition between states and showed as expected, the non-Markovian properties of this dynamics. We further simulate a copepod trajectory using an alternate renewal process for the generation of the sequence time series, and using a Brownian motion for the copepod motion during swimming periods.