Endothelialization of vascular surfaces. According to one aspect, the invention involves a technique for re-endothelializing an artery whose endothelial layer has been damaged by balloon angioplasty. The technique comprises, in one embodiment, introducing into the bloodstream of a patient, prior to performing the angioplasty, a quantity of a bispecific antibody, the bispecific antibody having a first antigen binding site directed against a surface marker common to both endothelial progenitor cells (EPCs) and endothelial cells (ECs) and having a second antigen binding site directed against a subendothelial epitope. The bispecific antibody is introduced in a quantity sufficient to bind a substantial percentage of circulating EPCs and circulating ECs. In this manner, once the angioplasty has been performed and the target epitopes on the subendothelium have been exposed, the bispecific antibodies that have already become bound to the circulating EPCs and ECs also then bind to the subendothelium. Thus seeded by the bound EPCs and ECs, the exposed subendothelium is covered after a short period of proliferation and differentiation.