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 &mdash；NHC(O)&mdash；, &mdash；C(O)&mdash；, &mdash；OC(O)&mdash；, &mdash；CH2&mdash； or &mdash；SO2&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 &mdash；NR6R7 group, or one &mdash；NR6R7 group and one or two hydroxyl groups； and R1 to R4 and R6 to R8 are as defined in the description.
