Antiviral cationic polyamines were prepared by modifying polyethylenimines with N-acylating agents that introduce a side chain comprising one or more carbons and at least one alcohol hydroxy group. The cationic polyamines can have a linear or branched polyethylenimine backbone structure. Preferably, the cationic polyamines comprise pendant monosaccharide groups, which can be introduced via a cyclic carbonate comprising a pendant protected monosaccharide (e.g., mannose) group. The cationic polyamines can be active and selective against a broad spectrum of viruses at low concentrations, and are generally non-toxic.