  We show that in low dimensional disordered conductors, the quasiparticle
decay and the relaxation of the phase are not exponential processes. In the
quasi-one dimensional case, both behave at small time as $e^{-
(t/\tau_{in})^{3/2}}$ where the inelastic time $\tau_{in}$, identical for both
processes, is a power $T^{2/3}$ of the temperature. This result implies the
existence of an unusual distribution of relaxation times that we obtain.
