The theory of anomalous skin effect in layered conductors with quasi-twodimensionalrnenergy spectnlll1 under high frequency electromagnetic wave propagationrnalong and perpendicular to the layers is studied in the account of Fermi-liquidrneffects in the absence of static magnetic field. The surface impedance, the conductivityrnand the skin depth are calculated explicitly for quadratic energy spectlUm andrnit is observed that the magnitudes differ in different orientations of the sample relativernto the direction of propagation of the wave. The dependence of these quantitiesrnon the Landau's correlation function is analyzed and they are compared qualitativelyrnwith the results in gas approximation theoretical results under the studies ofrnnormal metals