Abstract: The invention relates to N-desulfated and optionally 2-O-desulfated glucosaminoglycan derivatives, wherein at least part of the adjacent diols and OH/NH2 have been converted into the corresponding aldehyde, which aldehydes have been then reduced to the corresponding alcohol. These products are endowed with heparanase inhibitory activity and anti-tumor activity. Said glucosaminoglycan derivatives are obtained from natural or synthetic glucosaminoglycan, preferably from unfractionated heparin, low molecular weight heparins (LMWHs), heparan sulfate or derivatives thereof. The invention further relates to the process for preparation of the same and further to their use as active ingredients of medicaments, also in combination with known established drugs or treatments. The present invention further relates to a process for breaking the C2-C3 linkage of glucosamine residues of a glucosaminoglycan by oxidation of said glucosaminoglycan.