  We construct the effective action of certain exotic branes in the Type II
theories which are not predicted by their spacetime 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 SL(2,Z) triplet together with the D7-brane. We discuss why
this brane is not predicted by the Type IIB spacetime 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 SL(2,Z) moduli space. We discuss a similar relation between the
D6 and KK-6A branes and the D8 and KK-8A branes.
