Known hydroxyethylated and -propylated starch types for use as colloid osmotic agent in peritoneal dialysis or as volume replacement composition (plasma expander) have the disadvantage that complete degradation by amylase is not possible owing to the more or less extensive substitution by hydroxyethyl or hydroxypropyl groups. As a consequence thereof, residual fragments remain in the body and are eliminated only very slowly or are stored in various organs/tissues, especially with relatively high and/or long-term dosage. These disadvantageous properties can be very substantially avoided according to the invention with a highly branched, unsubstituted or low-substituted starch product, i.e. with a starch which has a significantly higher degree of branching than amylopectin, and has the degree of .alpha.-I,6 branching of glycogen, or exceeds the latter and--if substituted--has a degree of substitution MS of only up to 0.3.