There are many severe bacterial infections notorious for their ability to become resistant to clinically relevant antibiotics. Indeed, antibiotic resistance is a growing threat to human health, further exacerbated by the lack of new antibiotics. We now describe the practical synthesis of a series of substituted long linear polyamines that produce rapid antibacterial activity against both Gram-positive and Gram-negative bacteria, including meticillin-resistant Staphylococcus aureus. These compounds also reduce biofilm formation in Pseudomonas aeruginosa. The most potent analogues are thermine, spermine, and 1,12-diaminododecane homo- and heterodimeric polyamine succinic acid amides. They are of the order of activity of the aminoglycoside antibiotics kanamycin and tobramycin as positive controls. Their low human cell toxicity is demonstrated in ex vivo hemolytic assays where they did not produce even 5% hemolysis of human erythrocytes. These long, linear polyamines are a new class of broad-spectrum antibacterials active against drug-resistant pathogens.