Soluble highly branched glucose polymers having a reducing sugar content of less than 3.5%, preferably less than 1%, exhibit a alpha -1,6 glucosidic bonds rate of 20-30% and a molecular weight of 20/*10 3>； to 30/*10 3>；, determined by light diffusion. Independent claims are included for: (1) the preparation of the soluble highly branched glucose polymers comprising preparing an aqueous starch solution or its derivatives, preferably waxy starch (a dry matter of 10-30 wt.%), treating the solution using a branching enzyme then with a saccharification enzyme like amyloglucosidase (preferred) or -beta -amylase, fractionating to recover high molecular weight fractions and collecting the obtained highly branched glucose polymers； (2) a composition for food and pharmaceutical applications for human and animals, comprising the highly branched glucose polymers obtained by the process； and (3) a solution for peritoneal dialysis, comprising the soluble highly branched polymers as an osmotic agent.
