Performance of continuous cross-flow micellar-enhanced ultrafiltration (MEUF) method was investigated for the selective separation of copper (Cu2+) and cobalt (Co2+) from the aqueous phase using sodium dodecyl sulfate (SDS) as an anionic surfactant and iminodiacetic acid (IDA) as a chelating agent. Operating parameters such as operating time (10-120 min), cross-flow rate (100-250 mL/min), pH of the solution (2.8-5.6), molar concentration ratio of the chelating agent to metals (the C/M ratio, 0.5-2.5), molar concentration ratio of the surfactant to metals (the S/M ratio, 5-8) and mode of operation were studied to investigate the effectiveness of the process on selective separation. At optimal parameters, above 90% selective separation (Cu2+ in permeate and Co2+ in retentate) was achieved. Two methods were studied for the separation of Co2+ and SDS from retentate stream; acidification followed by UF and addition of chelating agent followed by UF with surfactant recovery of 75% and 83%, respectively, and Co going into the permeate.