Abstract: The present invention provides methods for manufacturing olefins such as ethylene and propylene from lower alkanes, that is, methane, ethane and/or propane, by oxidative dehydrogenation at elevated pressure. The olefins are selectively recovered from unconverted lower alkane feed and reaction byproducts by using a complexation separation, such as an absorption separation that uses aqueous silver nitrate as the complexation agent. Catalysts are used that give high selectivity for oxidative dehydrogenation of lower alkanes to olefins at elevated pressure, such as a nonstoichiometric rare earth oxycarbonate catalyst.