The invention relates to certain low-molecular weight sulphated polysaccharide derivatives of marine native exopolysaccharides (EPSs) excreted by mesophilic marine bacteria from a deep hydrothermal environment, wherein said derivatives can be obtained by means of a method which comprises a step of free radical depolymerisation of said native EPSs followed by a step of sulphating the resulting depolymerised derivatives. The present invention further relates to the use of said low-molecular weight sulphated polysaccharide derivatives as a wound-healing agent, particularly for preparing pharmaceutical compositions suitable for treating or preventing diseases of the connective tissues and particularly skin and gum tissues. The figure demonstrates how polysaccharide derivative GY 785 DRS according to the invention can stimulate fibroblast proliferation in latticed or reconstructed connective tissues at a concentration of 10 νg /ml.