  We provide an updated scan of the allowed parameter space of the two-loop
Zee-Babu model for neutrino mass. Taking into account most recent experimental
data on $\mu\to e\gamma$ as well as the mixing angle $\theta_{13}$ we obtain
lower bounds on the masses of the singly and doubly charged scalars of between
1 to 2 TeV, with some dependence on perturbativity and fine-tuning
requirements. This makes the scalars difficult to observe at LHC with 14 TeV
even with optimistic assumptions on the luminosity, and would require a
multi-TeV linear collider to see the scalar resonances. We point out, however,
that a sub-TeV linear collider in the like-sign mode may be able to observe
lepton flavour violating processes such as $e^- e^- \to \mu^- \mu^-$ due to
contact interactions induced by the doubly charged scalar with masses up to
around 10 TeV. We investigate the possibility to distinguish the Zee-Babu model
from the Higgs triplet model using such processes.
