  We estimate that the LHC could set bounds BR(Z -> mu^\pm e^\mp) < 4.1 *
10^{-7} and BR(Z -> tau^\pm mu^\mp)< 3.5 * 10^{-6} (at 95% C.L.) with 20
inverse fb of data at 8 TeV. A similar sensitivity can be anticipated for Z ->
tau^\pm e^\mp, because we consider leptonic tau decays such that Z -> tau^+
mu^- gives e^+ \mu^- +$ invisibles. These limits can be compared to the LEP1
bounds of order 10^{-5} to 10^{-6}. Such collider searches are sensitive to a
flavour-changing effective Z coupling which is energy dependent, so are
complementary to bounds obtained from tau to 3mu and mu to 3e.
