We construct the effective action of certain exotic branes in the Type II theories which are not predicted by their space-time supersymmetry algebras. We analyze in detail the case of the NS-7B brane, S-dual to the D7-brane, and connected by T-duality to other exotic branes in Type IIA: the KK-6A brane and the KK-8A brane (obtained by reduction of the M-theory Kaluza–Klein monopole and M9-brane, respectively). The NS-7B brane carries charge with respect to the S-dual of the RR 8-form, which we identify as a non-local combination of the electric–magnetic duals of the axion and the dilaton. The study of its effective action agrees with previous results in the literature showing that it transforms as an Full-size image (<1 K) triplet together with the D7-brane. We discuss why this brane is not predicted by the Type IIB space-time supersymmetry algebra. In particular we show that the modular transformation relating the D7 and NS-7B brane solutions can be undone by a simple coordinate transformation in the two-dimensional transverse space, equivalent to choosing a different region to parametrize the Full-size image (<1 K) moduli space. We discuss a similar relation between the D6 and KK-6A branes and the D8 and KK-8A branes.