Galactosyl-oligosaccharides (GOS) can be produced with native enzymes in Continuous Recycle Membrane Reactors (CRMR) or with immobilized enzymes in Plug Flow Bed Reactors (PFBR). In this paper a simple three kinetic constants model was implemented and used to define the optimal operation conditions to obtain a higher GOS yield. Experimental GOS yield and productivity obtained with CRMR were in good agreement with simulated results. The advantages of using single CRMR, two coupled CRMR and single CRMR coupled with Simulated Moving Bed Chromatography (SMBC), for product separation and continuous lactose recycling, were investigated with a modeling and experimental study. Experimental studies for single CRMR showed a 89 % higher amount of produced GOS than reports from immobilized enzymes in Plug Flow Bed Reactors (PFBR). Two coupled CRMR produced a 25 % higher amount of GOS than single CRMR. Simulated results with CRMR and SMBC for continuous lactose recycling showed 45% higher GOS amount than single CRMR. The results prove the feasibility and advantages of GOS production in single or series CRMR with native enzymes with or without lactose recycling.