  It is shown on the basis of the multiplicative renormalization-group method
of two-loop order that the low-energy effective Hamiltonian of a strongly
coupled local electron-phonon system is mapped to the two-channel Kondo model.
A phonon is treated as an Einstein oscillator with restricted Hilbert space
such that up to one-phonon process is taken into account. By eliminating the
high energy process of conduction electrons, it is shown that a certain class
of couplings between ion vibrations and conduction electrons is selectively
grown up. As a result the system is reduced to the two-channel Kondo model. The
crossover temperature $T_{\rm K}$ and the renormalized phonon frequency
$\Delta^{x}$ are expressed in terms of the mass ratio $m/M$, $m$ and $M$ being
the mass of electron and ion, and the electron-phonon coupling $g/D$, $D$ being
half the bandwidth of conduction electrons. The anomalous behaviors associated
with this renormalization can be mesuarable if the condition $T_{\rm
K}>\Delta^{x}$ is fulfilled. It is demonstrated that such condition is
satisfied when $g/D$ is sufficiently large but in a realistic range.
