  We investigate the conductivity in layered metals in magnetic field in the
weakly incoherent limit, when the interlayer transfer integral is smaller than
the Landau level broadening due to the impurity potential, but the interlayer
electron tunnelling conserves the intralayer momentum. It is shown that the
impurity potential has much stronger effect in this regime, than in the
quasi-2D metals in the coherent limit. The weakly incoherent regime has several
new qualitative features, not found in the previous theoretical approaches. The
background interlayer magnetoresistance in this regime monotonically grows with
increasing of magnetic field perpendicular to the conducting layers. The
effective electron mean free time is considerably shorter than in the coherent
regime and decreases with magnetic field. This enhances the role of higher
harmonics in the angular magnetoresistance oscillations and increases the
Dingle temperature, which damps the magnetic quantum oscillations.
