This paper presents the preparation and study of the properties of alginate materials, which were obtained on the basis of sodium alginate, activated carbon, cellulose, and calcium chloride. Alginate–carbon (AlgCa + C) and alginate–cellulose (AlgCa + Cel) composites, as well as pure calcium alginate (AlgCa) for comparative purposes, were obtained. Their textural (nitrogen adsorption/desorption isotherms), morphological (scanning electron microscopy), thermal (thermal analysis), and acid–base (pH drift method) properties, as well as the swelling index, were investigated. Additionally, to determine the adsorption properties, comprehensive equilibrium and kinetic studies of the adsorption of sodium salts of ibuprofen (IBP), diclofenac (D), and naproxen (NPX) from aqueous solutions on biocomposities were carried out. Adsorption isotherms were fitted using the Marczewski–Jaroniec isotherm equation (R2 = 0.941–0.988). Data on the adsorption rate were analyzed using simple kinetic equations, of which the best quality of fit was obtained using the multi-exponential equation (R2 − 1 = (3.9 × 10−4)–(6.9 × 10−4)). The highest obtained adsorption values were reached in systems with alginate–carbon composite and were 1.23 mmol/g for NPX, 0.81 mmol/g for D, and 0.43 mmol/g for IBP. The AlgCa + C material was characterized by a large specific surface area (1151 m2/g), a high degree of swelling (300%) and high resistance to high temperatures. Keywords: alginate–carbon/cellulose biocomposite; physicochemical characteristics; adsorption of drugs