The invention relates to soluble highly branched glucose polymers having a reducing sugar content of less than 1%, characterized in that they have a level of .alpha.-1,6 glucoside bonds greater than 10%, preferably of between 12 and 30%, a Mw value of between 0.35.times.10.sup.5 and 2.times.10.sup.5 daltons, and an osmolality having a value of between 1 and 15 mOsm/kg. The invention also relates to their method of production and their applications in the Paper-Carton, Textiles, Cosmetics, and particularly Pharmaceutical and Food industries, and still more particularly in the fields of enteral and parenteral nutrition, peritoneal dialysis as a glycemia inhibiting and/or regulating agent, as an energy source during physical activities and as a digestion regulating agent.