The question posed in the title has been addressed by studying the swelling of celluloses at 20°C by twenty protic solvents, including water; linear-and branched-chain aliphatic alcohols; unsaturated aliphatic alcohols, and alkoxyalcohols. The biopolymers investigated included microcrystalline cellulose, MC, native and never-dried mercerized cotton cellulose, cotton and M-cotton, and native and never-dried mercerized eucalyptus cellulose, eucalyptus and M-eucalyptus, respectively. In most cases, better correlations with the physico-chemical properties of the solvents were obtained when the swelling was expressed as number of moles of solvent/ anhydroglucose unit, nSw, rather than as % increase in sample weight. The descriptors employed in these correlations included, where available, Hildebrand's solubility parameters, Gutmann's acceptor and donor numbers, solvent molar volume, V S , as well as solvatochromic parameters. The latter, employed for the first time for correlating the swelling of biopolymers, included empirical solvent polarity, E T (30), solvent ''acidity'', a S , ''basicity'', b S , and dipolarity/ polarizability, p S * , respectively. Small regression coefficients and large sums of the squares of the residues were obtained when values of nSw were correlated with two solvent parameters. Much better correlations were obtained with three solvent parameters. The most statistically significant descriptor in the correlation equation depends on the cellulose, being p S * for MC, cotton, and eucalyptus, and V S for M-cotton and M-eucalyptus. The best correlations were obtained with the same set of four parameters for all celluloses, namely, solvent pKa (or a S ) b S , p S * , and V S , respectively. These results indicate that the supra-molecular structure of the biopolymer, in particular the average sizes of crystallites and micro-pores, and the presence of its chains in parallel (cellulose I) or anti-parallel (cellulose II) arrangements control its swelling. At least for the present biopolymer/solvent systems, use of solvatochromic parameters is a superior alternative to Hildebrand's solubility parameters and/or Gutmann's acceptor and donor numbers. The relevance of these results to the accessibility of the hydroxyl groups of cellulose, hence to its reactivity, is briefly discussed.