This contribution presents the first measurement of the rate of exciton-exciton annihilation in J aggregates for which a strong nonmonotonous temperature dependence was found. Annihilation is suppressed at low temperature (T < 20 K), very pronounced in the temperature region of 20-70 K, and it decreases again while temperature increases from 70 to 300 K. We suggest that an exciton hopping process occurs at low temperature (T < 20 K), a coherent wave-packet-like exciton transport occurs in the intermediate temperature region (20-70 K), and a strong exciton scattering occurs on optical phonons at high temperatures (70-300 K). The exciton migration properties in J aggregates were compared with those in molecular crystals.