  We consider a Tsallis holographic dark energy model with interaction between
dark energy and matter. The density of dark energy is taken as $\rho_d \sim
3C^2/L^{4-2\gamma}$, where $C$, $\gamma$ are constants. The event horizon is
chosen as the characteristic scale $L$. The cosmological dynamics of the
universe are analyzed, with special attention paid to the possibility of
crossing the phantom line $w_{eff}=-1$. It is shown that for certain values of
parameters this may occur not only once, but also twice.
