1,6-Anhydro-D-hexofuranoses, such as 1,6-anhydro-β-D-glucofuranose (1), 1,6-anhydro-β-D-mannofuranose (2), and 1,6-anhydro-α-D-galactofuranose (3), were polymerized using a thermally induced cationic catalyst in dry propylene carbonate to afford hyperbranched polysaccharides (poly1-3) with degrees of branching from 0.40 to 0.46. The weight-average molecular weights of poly1-3 measured by multiangle laser light scattering varied in the range from (1.02 to 5.84) × 10(4) g·mol(-1), which were significantly higher than those measured by size exclusion chromatography. The intrinsic viscosities ([η]) of poly1-3 were very low in the range from 4.9 to 7.4 mL·g(-1). The exponent (α) in the Mark-Houkwink-Sakurada equation ([η] = KM(α)) of the polymers was 0.20 to 0.33, which is <0.5. The steady shear flow of poly1-3 in an aqueous solution exhibited a Newtonian behavior with steady shear viscosities independent of the shear rate. These viscosity characteristics were attributed to the spherical structures of hyperbranched polysaccharides in an aqueous solution. Poly1-3 contained a high portion of terminal units of 31-43 mol % nonreducing D-hexopyranosyl and D-hexofuranosyl units, in which the D-hexofuranosyl units were 20-44 mol %. Moreover, poly1 and poly2 showed a strong interaction to Concanavalin A due to the cluster effect or multivalent effect of numerous nonreducing saccharide units on their surfaces with binding constants in the range from 1.7 × 10(4) to 2.7 × 10(5) M(-1).