<p>The adsorption of Re^VII was estimated for polyethyleneimine (PEI), polyallylamine (PAA), and polyaminostyrene (PAST) possessing different Brønsted basicity. A high adsorption of Re^VII (up to 97%) from the acetate buffer solution was observed in the pH range of 2.8–3.1 for PEI and PAST, and in the pH range of 2.8–5.2 for PAA. The kinetic data indicated a mixed diffusion mode for the sorption with a significant contribution of the step of chemical interaction between Re^VII and functional groups of the sorbents. Rapid establishment of the equilibrium (within 5–10 min) was observed for all the sorbents in contrast with industrial anion exchangers used as the reference. The isotherms plotted for the sorption of Re^VII within the concentration range of 5–400 mg L⁻¹ were mathematically processed within the framework of the Langmuir, Freundlich, and Dubinin—Radushkevich models. The affinity of Re^VII towards the sorbents decreases in the series of PAA &gt; PEI &gt; PAST. The values calculated for the sorption capacity of PAA (1.81 mmol g⁻¹), PEI (2.43 mmol g⁻¹), and PAST (0.98 mmol g⁻¹) were not inferior to the corresponding values for modern weakly basic sorbents. The presence of a 200 fold excess of Cu^II in the solution caused virtually no effect on the sorption of Re^VII. At 200 fold excess of Mo^VI, the adsorption of Re^VII on PAST (<i>A</i> = 94%) and PEI (<i>A</i> = 85%) remained at a high level, whereas in the case of PAA, the effect of Mo^VI was more significant decreasing the sorption by 36.5%.</p>