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The hydrophilic and hydrophobic single-walled carbon nanotube membranes were prepared and progressively applied in sorption, filtration, and pertraction experiments with the aim of eliminating three antibiotics—tetracycline, sulfamethoxazole, and trimethoprim—as a single pollutant or as a mixture. The addition of SiO₂ to the single-walled carbon nanotubes allowed a transparent study of the influence of porosity on the separation processes. The mild oxidation, increasing hydrophilicity, and reactivity of the single-walled carbon nanotube membranes with the pollutants were suitable for the filtration and sorption process, while non-oxidized materials with a hydrophobic layer were more appropriate for pertraction. The total pore volume increased with an increasing amount of SiO₂ (from 743 to 1218 mm³/g) in the hydrophilic membranes. The hydrophobic layer completely covered the carbon nanotubes and SiO₂ nanoparticles and provided significantly different membrane surface interactions with the antibiotics. Single-walled carbon nanotubes adsorbed the initial amount of antibiotics in less than 5 h. A time of 2.3 s was sufficient for the filtration of 98.8% of sulfamethoxazole, 95.5% of trimethoprim, and 87.0% of tetracycline. The thicker membranes demonstrate a higher adsorption capacity. However, the pertraction was slower than filtration, leading to total elimination of antibiotics (e.g., 3 days for tetracycline). The diffusion coefficient of the antibiotics varies between 0.7–2.7 × 10⁻¹⁰, depending on the addition of SiO₂ in perfect agreement with the findings of the textural analysis and scanning electron microscopy observations. Similar to filtration, tetracycline is retained by the membranes more than sulfamethoxazole and trimethoprim.