  We evaluate the decays $\ell_1^\pm \to \ell_2^\pm \gamma$, $Z \to \ell_1^+
\ell_2^-$, and $h \to \ell_1^+ \ell_2^-$, where $\ell_1$ and $\ell_2$ are
charged leptons with different flavours and $h$ is the scalar particle with
mass 125.25 GeV, in a two-Higgs-doublet model where all the Yukawa-coupling
matrices conserve the lepton flavours but the Majorana mass terms of the
right-handed neutrinos break the flavour lepton numbers. We find that (1) the
decays $\ell_1^\pm \to \ell_2^\pm \gamma$ require large Yukawa couplings and
very light right-handed neutrinos in order to be visible, (2) the decays $Z \to
\ell_1^+ \ell_2^-$ will be invisible in all the planned experiments, except in
a very restricted range of circumstances, but (3) the decays $h \to \ell_1^+
\ell_2^-$ may be detected in future experiments for rather relaxed sets of
input parameters.
