The present invention is a process for removing alkynes and/or dienes from an olefin product stream withdrawn from an oxygenate-to-olefins reactor. The process comprises hydrogenating a first olefin stream that has alkynes and/or dienes in the presence of excess hydrogen and a first hydrogenation catalyst. The hydrogenation of the first olefin stream produces a second olefin stream that has unreacted hydrogen. The second olefin stream is contacted with a second hydrogenation catalyst producing a third olefin stream. The third olefin stream has low levels of hydrogen and alkynes and/or dienes.