  We discuss sensitivities to lepton flavor violating (and conserving)
interactions at future muon colliders, especially at $\mu^+\mu^+$ colliders.
Compared with the searches for rare decays of $\mu$ and $\tau$, we find that
the TeV-scale future colliders have better sensitivities depending on the
pattern of hierarchy in the flavor mixings. As an example, we study the case
with the type-II seesaw model, where the flavor mixing parameters have direct
relation to the neutrino mass matrix. At a $\mu^+ \mu^+$ collider, the number
of events of the $\mu^+ \mu^+ \to \mu^+ \tau^+$ process can be larger than
$\mathcal{O}(100)$ with the center of mass energy $\sqrt s = 2$ TeV, and with
an integrated luminosity ${\cal L} = 1$ ab$^{-1}$, while satisfying bounds from
rare decays of $\mu$ and $\tau$. We discuss impacts of the overall mass scale
of neutrinos as well as CP violating phases to the number of expected events.
