Acetylene present in olefin plant process streams is hydrogenated by: (i) separating feedstream (2) in a depropaniser (36) into 4+C-rich liquid stream (37) and lighter vapour stream (38); (ii) mixing the vapour stream with reflux liquid (62) and passing this mix through a mixed phase hydrogenator (MPH; 54) to selectively hydrogenate the acetylene; (iii) passing effluent from (ii) (58) to a vapour phase hydrogenator (VPH; 70); and (iv) subsequent separation of effluent from (iii) (72).    Also claimed is a fuller similar process incorporating the extra steps of: (a) initial chilling (4,8) and separation (12) of the process stream to produce liquid (26) and vapour (34) feeds for the depropaniser; (b) cooling and partial condensation (40) of the lighter stream from the depropaniser before passing to the MPH; (c) separating MPH product to provide depropaniser reflux liquid (60) and VPH feed (68); and (d) chilling and condensation (74, 78) of VPH product and separation (82) into a recycle (86) for use as depropaniser reflux liquid (94) and MPH feedstream make-up (96) and a product gas (84). The concept of hydrogenation between depropanising and subsequent separation is also independently claimed. Additionally claimed is a similar process to the above but without the depropanising step.    Pref. feedstream to process is steam pyrolysis product or catalytic cracker off-gas and can comprise C4H10, C4H8, C3H8, C3H6, C2H6, C2H4, C2H2, CH4, H2 and/or CO. Depropanising carried out at 150-300 psia. Further separation can pref.include de-ethanisation and/or de-methanisation.Pref. MPH operates at 10-400 C and 200-600 psia using a gp VIII metal catalyst (eg Raney-Ni, Pd/alumina, Ru/alumina and/or NiAs/alumina). VPH operates at 10-2000 C and 200-600 psia using a gp VIII metal catalyst, pref at 0.01-1% on a support (eg any of those specified for MPH and, esp, 0.1% Pd on low surface area granular alumina).    ADVANTAGE -   Acetylene is hydrogenated without requiring external solvent in a process which is more tolerant of variations in C2H2 and/or CO concns in temps and which shows improved selectivity and safety and has simplified vapour clean-up.