  A long-lived very light pseudoscalar boson would favor lepton flavor
violating transitions of charged leptons. Its implications on the l_i --> l_j
\gamma \gamma, and l_i --> l_j e^+ e^- transitions are investigated. Assuming 2
m_e < m_\phi <m_\mu, it is found that the inequality B(l_i --> l_j \gamma
\gamma)<B(l_i --> l_j e^+ e^-) is hold. The experimental constraints on the
decays l_i --> l_j \gamma, l_i --> l_j l_k l_k, and l_i --> l_j \gamma \gamma
are used to bound the \phi l_i l_j couplings.
