Abstract: The activity and cell membrane affinity of certain antiviral multiple branch peptide constructions, including those known from WO 95/07929, WO 98/29443 and WO 03/95479, can be improved by bonding to the C-end of the peptide a terminator which is either (a) an ?-amino-fatty acid having from 4 to 10 carbon atoms and from 0 to 2 carbon-carbon double bonds or (b) a peptidic cell membrane penetrating agent. The improvement is so marked that in some cases the number of branches can be reduced, sometimes to a single branch, and/or that the branches may be shortened. The preferred ?-amino-fatty acids are ?-aminobutyric acid, ?-aminovaleric acid and ?-aminocaproic acid. The peptidic cell membrane penetrating agent is suitably a TAT-derived peptide, penetratin® or Kpam.