Higher molecular weight hydrocarbon compounds or oxygenates are produced from a gas comprising methane in a process comprising the steps of generating synthesis gas (“syngas”) comprising carbon monoxide and hydrogen by reaction of a gas comprising methane with steam and/or an oxidant gas comprising oxygen, producing higher molecular weight hydrocarbon compounds or oxygenates in a syngas conversion process, removing offgas comprising unreacted hydrogen and unreacted carbon monoxide from said syngas conversion process and separating cryogenically unreacted hydrogen from said offgas or from a gas derived therefrom to produce separated hydrogen product that is substantially free of unreacted carbon monoxide and a first cryogenic liquid comprising unreacted carbon monoxide. The unreacted hydrogen is preferably separated from the offgas in a liquid methane wash column.