Oligomerization of C4-C5 olefins and olefin mixtures has been investigated in the presence of a supported ionic liquid phase (SILP) catalyst, obtained by the physisorption of 1-(4-sulfobutyl)-3-methylimidazolium trifluoromethanesulfonate on silica. Surface properties of the SILP phase were determined from the experimental data of their nitrogen adsorption/desorption isotherms. Fresh and spent catalyst were characterised by C-13- and Si-29-CP MAS NMR spectroscopy and thermogravimetric analysis. Reactivity of alkenes followed the awaited order of isobutene > but-1-ene > pent-1-ene. The main products of oligomerization of hydrocarbon mixtures, modelling the C4-C5 fraction of waste polyethylene cracking products, were isoolefins in the boiling point range corresponding to kerosene fraction components, which is applicable as jet fuel after hydrotreatment. Stability and recyclability of the catalyst could greatly be enhanced by a pretreatment of the fresh catalyst, carrying out an oligomerization experiment with pure isobutene.