Oligomerization reactions of ethene, propene, isobutene, and 2-methyl-butene-1 on zeolite H-ZSM-5 at 300 and 373K were investigated using high-resolution solid-state 13C-NMR spectroscopy. It is shown that at 300K only linear oligomers are formed, while at 373K some branching is observed. Thus at 300K on zeolite H-ZSM-5 initially formed branched oligomers are stretched in consecutive isomerization reactions. Differential scanning calorimetry experiments on the adsorption of n-hexane and isohexane show that the specific pore dimensions of zeolite ZSM-5 are responsible for an increased heat of adsorption of linear paraffins compared to branched paraffins. A reaction scheme is presented to explain the experimental data.