  We consider a theoretical problem of electron-electron scattering time in a
quasi-one-dimensional (Q1D) conductor in a magnetic field, perpendicular to its
conducting axis. We show that inverse electron-electron scattering time becomes
of the order of characteristic electron energy, $1/\tau \sim \epsilon \sim T$,
in a high magnetic field, directed far from the main crystallographic axes,
which indicates breakdown of the Fermi liquid theory. In a magnetic field,
directed close to one of the main crystallographic axis, inverse
electron-electron scattering time becomes much smaller than characteristic
electron energy and, thus, applicability of Fermi liquid theory restores. We
suggest that there exist crossovers between Fermi liquid and some non Fermi
liquid states in a strong enough tilted magnetic field. Application of our
results to the Q1D conductor (Per)$_2$Au(mnt)$_2$ shows that it has to be
possible to observe the above mentioned phenomenon in feasibly high magnetic
fields of the order of $H \geq H^* \simeq 25 \ T$.
