The invention relates to the use of hyperbranched amylopectin which has an average branch degree of between >10 and 25 mol % and a molecular weight (Mw) ranging from 40.000-800.000 Dalton and the derivatives thereof in methods for surgical or therapeutic treatment of human or animal bodies or in a diagnostic method, preferably as a plasma volume expander. Plasma volume expanders based on hydroxy-ethylated amylopectin have, as a result of hydroxy ethylation, hitherto exhibited the disadvantage of incomplete metabolism and thus temporary tissue storage which is linked to side-effects. According to the invention, novel plasma expanders based on polysaccharides which do not exhibit the same disadvantages as the former are provided. Improved, completely metabolised plasma expanders based on hyperbranched amylopectin which can be obtained therefrom so that native plant-amylopectins are altered-by transglycosylation in such a way the adjustable, high degree of branching enables control of the serum-.alpha.-amylase decomposition so that no or only a very insignificant degree of hydroxy ethylation is necessary.