The photoinduced E -> Z isomerization of azobenzene is a prototypical example of molecular switching. On the way toward rigid molecular rods such as those for opto-mechanical applications, multiazobenzene structures have been suggested in which several switching units are linked together within the same molecule (Bleger et al., J. Phys. Chem. B 2011, 115, 9930-9940). Large differences in the switching efficiency of multiazobenzenes have been observed, depending on whether the switching units are electronically decoupled or not. In this paper we study, on a time-resolved molecular level, the E -> Z isomerization of the simplest multiazobenzene, bisazobenzene (BAB). Two isomers (ortho- and para-BAB), differing only in the connectivity of two azo groups on a shared phenyl ring will be considered.To do so, nonadiabatic semiclassical dynamics after photo-excitation of the isomers are studied by employing an "on-the-fly", fewest switches surface hopping approach. States and couplings are calculated by Configuration Interaction (CI) based on a semiempirical (AM1) Hamiltonian (Persico and co-workers, Chem. Eur. J. 2004, 10, 2327-2341). In the case of para-BAB, computed quantum yields for photoswitching are drastically reduced compared to pristine azobenzene, due to electronic coupling of both switching units. A reason for this (apart from altered absorption spectra and reduced photochromicity) is the drastically reduced lifetimes of electronically excited states which are transiently populated. In contrast for meta-connected species, electronic subsystems are largely decoupled, and computed quantum yields are slightly higher than that for pristine azobenzene because of new isomerization channels. In this case we can also distinguish between single- and double-switch events and we find a cooperative effect: The isomerization of a single azo group is facilitated if the other azo group is already in the Z-configuration.