The invention relates to N-desulfated and optionally 2-O-desulfated glycosaminoglycan derivatives, wherein at least part of the adjacent diols and OH/NH 2 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 glycosaminoglycan derivatives are obtained from natural or synthetic glycosaminoglycan, 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 C 2 -C 3 linkage of glycosamine residues of a glycosaminoglycan by oxidation of said glycosaminoglycan.