The results of the investigation showed that second-order kinetics govern the adsorption process, and the corresponding rate constants were found. To evaluate the parameters related to the adsorption process, the adsorption equilibrium was examined using a variety of mathematical models, such as the Langmuir, Freundlich, Temkin, and Dubinin-Radushkevich isotherm models. The Langmuir isotherm was found to be the best appropriate among all models for describing the adsorption of Cu2+ and Ni2+ ions using bio-nanocomposite beads. The positive values of ΔH° indicate that the adsorption is physical and endothermic, in agreement with experimental results. The negative value of ∆G° shows that the adsorption process is spontaneous. Positive ΔS° values indicate increased randomness at the solid/liquid interface, during adsorption of Cu2+ and Ni2+ cations onto the engineered bio-nanocomposite. The maximum adsorbed amounts of metal ions by the bio-nanocomposite used were 370.37 mg/g for Ni2+ and 454.54 mg/g for Cu2+ from single system. For the binary system, according to the Langmuir isotherm, the maximum adsorbed amounts of Ni2+ and Cu2+ were 357.14 mg/g and 370,37 mg/g, respectively. There is proof that Alginate-Moroccan clay bio-nanocomposites can serve as a different, less expensive source of sorbents for the removal of metal ions from single and binary systems.