Compounds exhibiting angiogenic properties incorporating the structure of Formula I: R.sub.3--NH--NH--C(.dbd.O)--R.sub.2--P--R.sub.1 (I) wherein P is a water-soluble, biodegradable polymer, R.sub.1 is hydrogen, lower alkyl, lower alkoxy or --R.sub.2--C(.dbd.O)--NH--NH--R.sub.3; each R.sub.2 is independently --CH.sub.2--, --NH-- or O; and each R.sub.3 is independently hydrogen or a residue of a naturally occurring alpha-L-amino acid or dipeptide thereof. Polymer networks crosslinked with hydrazide compounds are also disclosed, together with implantable medical devices incorporating the compounds and crosslinked polymers, and angiogenesis-promoting treatment methods, including wound-treatment methods.