A method is described for treating a microbial infection with a peptide whoseamino acid sequence has a formula selected from the group consisting of: (a)Bn1-Z (b) Bn1-Z-Bn2 and (c) Z-Bn1 wherein B is a basic amino acid residuen1 and n2 are 1 to 6 and Z is a sequence of about 11 to about 24 amino acidresidues, the sequence having an average hydrophobicity value of at least 0.3,and preferably at least 0.4. These peptides show antimicrobial activityagainst microorganisms including both Gram-positive and Gram-negative bacteria.