Stainless steel, the structural metals of Groups II, III and IV and their alloys are lubricated with a composition which consists or comprises a diester of formula <FORM:1079566/C4-C5/1> where X is <FORM:1079566/C4-C5/2> R is C6-C20 alkyl, methyl C6-C20, alkyl or ethyl C6-C20 alkyl and R1 is C12-C20 alkyl, methyl C12-C20 alkyl or ethyl C12-C20 alkyl. Diesters specified are dilauryl and distearyl maleate and fumarate, dioctyl and dipalmityl itaconate, lauryl stearyl maleate and itaconate, tridecyl, 2-ethylhexyl and 2-octyl-stearyl maleate, 1-nonyl stearyl and i-nonyl lauryl fumarate, 2-octyl stearyl itaconate and mixed esters where the average mol. proportion of R or R1 may vary from 0.1-1.9 mols. per mol. of acid. The composition may contain a mineral oil; a fatty oil; degras; polysiloxanes (many specified which may or may not contain halogen); diesters of formula (R2OOC)R(COOR1) where R is a C2-C8 aliphatic or cycloaliphatic hydrocarbon radical which may contain oxygen or sulphur, R1 and R2 are the same or different and are branched chain alkyl or alkyl substituted cycloalkyl radicals of at least 4 C atoms, e.g. diesters derived from succinic, maleic, pyrotartaric, glutaric, adipic, pimelic, suberic, azelaic, sebacic, pinic, thiopropionic and oxypropionic acids; esters derived from a polyhydric alcohol and a monocarboxylic acid, e.g. ethylene glycol or pentaerythritol with caproic, pelargonic, capric, lauric, myristic, palmitic or stearic acids; complex esters; polymeric hydrocarbons; polyglycols; propylene oxide-tetrahydrofuran copolymers; polyaryl ethers; silanes, sulphenylenes; organo-silicates; disiloxanes; fluorcarbon oils; tetra-substituted ureas; dimethyl-cyclohexyl phthalate and trioctyl phosphate. The composition may also contain the usual phenolic and amine anti-oxidants, phenothiazine, iron octoate, a -aminoanthraquinone, benzanthracene, fluoranthracene, a -naphthylamine, N,N1-dinaphthylphenylenediamine, benzoguanamine, di - tert-butylhydroquinone, quinazarine, Indanthrene blue, mica, graphite and thickeners, e.g. lithium hydroxystearate, silica aerogel, a ureide or urethane.