Exciton-exciton annihilation is implied to be in fact a unique channel of exciton degradation in linear molecular aggregates and conjugated polymers as the pump intensity rises. However, at low temperatures, excitons represent rather immobile than movable quasi-particles due to the localization effect. We analyze possible channels of exciton-exciton annihilation, which seem to be natural ones under the conditions of localization and low temperature, and calculate the corresponding rates. (C) 2000 Elsevier Science B.V. All rights reserved.