The kinetics of the delayed luminescence arising from correlated coherent many-soliton states in low-dimensional macromolecular systems, is calculated and shown to be different from the one arising from independent soliton states. The correlation between coherent electron states is essential at relatively high levels of excitation in the presence of very long macromolecules in a system. These conditions can be fulfilled in such biological systems, like algae Acetabularia Acetabulum. The cytoskeleton of this unicellular alga contains macromolecular structures (actin filaments, microtubules, etc.) of the length of several hundreds angstroms and more, in which many-soliton coherent states can exist. Indeed, the correlated coherent model is shown to give better fit of the experimental data for this type of algae in a wide range of intensities of the stimulating light, as compared with the model of noncorrelated solitons. The nonlinearity of the dependence of delayed luminescence intensity on the level of excitation increases with the increase of correlation between solitons.