A simple model for aggregate formation in cellulose solutions is presented. Owing to a strong tendency of hydrogen-bond formation among the cellulose molecules, aggregation does not lead to a completely random arrangement of the molecules. In a core, parts of the chain molecules are laterally aligned. This core is surrounded by disordered regions that give rise to the formation of coronas under the action of solvent molecules while the core is completely immiscible with the solvent. Therefore, the aggregates can be seen as fringed micelles. The equilibrium structure of these micelles, number of aggregated chains and size of the coronas, is discussed as a function of the interfacial tension between core and solvent. It turns out that both number of aggregated chains and thickness of the coronas increase with increasing interfacial tension. In perfect solutions of the micelles, these quantities also increase with cellulose concentration. If one admits attractions between coronas of different micelles, as a small perturbation, clustering of micelles might be induced. This may cause phase instability of the particle phase which results in the coexistence of a diluted and a more concentrated solution.