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We describe application of theory and kinetic modeling to study transport of basic anions by the small synthetic molecules. The findings should equip researchers in the particular field with a tool necessary to address an essential question: whether a given anion transporter facilitates permeation of F, CHCOO, N, and SCN across biological membrane or it does not. The basic anions undergo hydrolysis and conjugate acids (HAnion) are permeant species. However, because methods to quantitatively account for HAnion transport do not exist, traditionally, the phenomenon is also treated as non-existing. When the relative activities and selectivity of the synthetic anionophores are evaluated, basic and non-basic anions are regarded in the same exact way. Here, we show that HAnion and H/OH transport proceed on the same time scale as the anion exchange, nevertheless, comprehensive kinetic study could provide solution to the problems at hands, such as selective transport of HCO or F anions. We also use theory and modeling to study other questions of particular concern: transport of OH and H ions, facilitated by the small synthetic anionophore, origin of modified anti-Hofmeister selectivity, multi-ion hopping, and anomalous mole-fraction effect in the synthetic ion channels. We do not need to model kinetics in a synthetic channel with multiple ion binding sites. Instead, we 'test' the most simple anionophore, a lipophilic electroneutral carrier with Hofmeister-like selectivity, in the classical assays as 'presumably, Cl/OH antiporter.' The implications of findings to the particular field and beyond are discussed. Graphical Abstract: [Figure not available: see fulltext.]. [ABSTRACT FROM AUTHOR]