Despite frequent use and long history of the measurement of the erythrocyte sedimentation rate (ESR) in clinical practice the coherent theory of this process is still lacking. Analysis of the "aggregation theory" of red blood sedimentation in tubes is performed. This theory claims that erythrocytes in resting blood aggregate due to adhesion provided by macromolecules adsorbed on their surfaces, and that their aggregates sediment according to the Stokes' law. Data obtained in studies of detailed dynamics of red blood sedimentation and direct observations of erythrocytes association and rouleaux dissociation, do not support the "aggregation theory". A model of red blood sedimentation suggested in 1928 by S. D. Balakhovskiĭ is considered. According to this model under the conditions of ESR measurement erythrocytes rapidly associate and from rouleaux network. The course and character of red blood sedimentation is determined by the network stability against packing down. To explain the mechanism of erythrocytes association in aqueous solutions of various water soluble polymers including blood plasma we suggest a model based on the phenomenon of phase separation in aqueous polymer solutions. We demonstrate that these two models taken together agree much better than the "aggregation" theory with the experimental results including data on the role of cell metabolism in the association phenomenon. This new model allows to explain many critical phenomena observed in the processes of erythrocytes association-dissociation both in the resting and flowing blood and attract attention to the cooperative nature of this process as well as the process of red blood sedimentation.