A process for converting light paraffins (especially C3-C5) to middle distillate and higher boiling range liquid hydrocarbons by (1) oxygen or air oxidation of iso-paraffins to alkyl hydroperoxides; (2) conversion of alkyl hydroperoxides to dialkyl peroxides; (3) radical coupling of paraffins using the dialkyl peroxides as radical initiators forming heavier hydrocarbon products; and (4) fractionation of the heavy hydrocarbon products. The net reaction is catalytically converting light paraffins to heavier hydrocarbons using oxygen or air to effect the conversion.