The possibility of concentration of the heavy metals using cobalt as an example has been studied. It has been actualized in the membrane reactor at a combination of sorption onto the clay mineral or a cation-exchange resin and the following pressure-driven membrane separation of a mixture. The retention coefficient of Co(II) ions by the OPAM-KN membrane under the quasi-steady mode of long-term operation reaches 0.92 and 0.98 when the montmorillonite clay mineral and KU-2-8n cation-exchange resin is used, respectively. This coefficient is essentially lower when the UPM-20 has been used, viz., it is 0.08 and 0.60 in cases of the former and the latter, respectively. An effect of the sorbents differing in their nature on the purification/concentration process in the so-called hybrid method was determined. Such a conclusion has been reached based on the data on the water state in the dynamic membranes formed by a clay mineral or a cation-exchange resin onto the surface of the supporting OPAM-KN and UPM-20 membranes. The information on the water state has been obtained by the differential-scanning calorimetry method.