  Magnetic quantum oscillations (MQO) are traditionally applied to investigate
the electronic structure of metals. In layered quasi-two-dimensional (Q2D)
materials the MQO have several qualitative features giving additional useful
information, provided their theoretical description is developed. Within the
framework of the Kubo formula and the self-consistent Born approximation, we
reconsider the phase of beats in the amplitude of Shubnikov oscillations of
interlayer conductivity in Q2D metals. We show that the phase shift of beats of
the Shubnikov (conductivity) oscillations relative to the de Haas - van Alphen
(magnetization) oscillations is larger than expected previously and, under
certain conditions, can reach the value of $\pi/2$, as observed experimentally.
We explain the phase inversion of MQO during the 3D - 2D crossover and predict
the decrease of relative MQO amplitude of interlayer magnetoresistance in a
strong magnetic field, larger than the beat frequency.
