This invention provides a method for inhibiting or preventing the abnormal growth of cells, including transformed cells, by administering an effective amount of O-acylated heparin derivative. Abnormal growth of cells refers to cell growth independent of normal regulatory mechanism (e.g. loss of contact inhibition). This includes the abnormal growth of: (1) tumor cells (tumors); (2) benign and malignant cells of other proliferative disease in which aberrant cellular proliferation occurs; (3) aberrant smooth muscle cell proliferation, such as might occur following treatment for coronary atherosclerosis such as angioplasty or the insertion of a stent into an occluded vessel.