  Within the MSSM, we have evaluated the decay rates for the lepton flavour
violating Higgs boson decays (LFVHD) $h \rightarrow l_i l_j$ where $l_{i,j}$
are charged leptons and $i\neq j$. This has been done in a model independent
(MI) way as well as in supersymmetric high scale seesaw models, in particular
Type I see-saw model. Lepton flavour violation (LFV) is generated by
non-diagonal entries in the mass matrix of the sleptons. In a first step we use
the model independent approach where LFV (off-diagonal entries in the mass
matrix) is introduced by hand while respecting the direct search constraints
from the charged lepton flavor violating (cLFV) processes. In the second step
we use high scale see-saw models where LFV is generated via renormalization
group equations (RGE) from the grand unification scale (GUT) down to
electroweak scale. cLFV decays are the most restrictive ones and exclude a
large part of the parameter space for the MI as well as the high scale see-saw
scenarios. Due to very strict constraints from cLFV, it is difficult to find
large corrections to LFVHD. This applies in particular to $h \rightarrow \tau
\mu$ where hints of an excess have been observed. If this signal is confirmed,
it could not be explained with the models under investigation.
