  We establish an explicit correspondence between perturbative and
nonperturbative results in the problem of quantum decoherence in disordered
conductors. We demonstrate that the dephasing time $\tau_{\phi}$ cannot be
unambiguously extracted from a perturbative calculation. We show that the
effect of the electron-electron interaction on the magnetoconductance is
described by the function $A_d(t)\exp (-f_d(t))$. The dephasing time is
determined by $f_d(t)$, i.e. in order to evaluate $\tau_{\phi}$ it is
sufficient to perform a nonperturbative analysis with an exponential accuracy.
The effect of interaction on the pre-exponent $A_d(t)$ is important if one
calculates the interaction-dependent part of the weak localization correction
for strong magnetic fields. The zero temperature dephasing time drops out of
this correction in the first order due to the exact cancellation of the linear
in time $T$-independent contributions from the exponent and the pre-exponent.
Nonlinear in time $T$-independent contributions do not cancel out already in
the first order of the perturbation theory and yield an additional contribution
to dephasing at all temperatures including T=0.
