A process is provided for conversion of a feedstock, in particular a hydrocarbon feedstock such as methane or natural gas, in which a reactive mixture containing the feedstock is prepared and fed to a reaction zone. A reaction is initiated in the reactive mixture within the reaction zone so as to generate a conversion wave of increased temperature and pressure. The conversion wave is allowed to pass through the reaction zone, from where converted feedstock is recovered. An apparatus for carrying out the process is also provided. The process operates with a high conversion and selectivity to desirable products and is particularly suitable for the conversion of methane to carbon monoxide and hydrogen.