Provided are compounds, the use of the said compounds in treatment, for example treatment of microbial infections, particularly by Gram negative bacteria. The compounds are polymyxin-based and are represented by the formula (I): and pharmaceutically acceptable salts thereof, where X is &mdashNHC(O)&mdash, &mdashC(O)&mdash, &mdashOC(O)&mdash, &mdashCH2&mdash or &mdashSO2&mdash R5 represents C0-12 alkyl(C4-6 heterocyclyl), or C2-12 alkyl or C0-12 alkyl(C3-8 cycloalkylyl). and the alkyl or cycloalkylyl bears one, two or three hydroxyl groups, or a &mdashNR6R7 group, or one &mdashNR6R7 group and one or two hydroxyl groups and R1 to R4 and R6 to R8 are as defined in the description.
