New lipopolyamines of general formula (I), their salts, their preparation and their use. ##STR1## n=1 to 5 and m=2 to 6 R represents a radical ##STR2## (R.sub.1 and R.sub.2 : aliphatic radical containing 12 to 22 carbon atoms; R: hydrogen atom or alkyl radical optionally substituted with phenyl), or a radical ##STR3## (X=CH.sub.2, CO; R.sub.3 and R.sub.4 aliphatic radical containing 11 to 21 carbon atoms), their preparation and their use.The lipopolyamines of general formula (I) are especially useful as vectors for the transfection of eukaryotic cells.