INTRODUCIONAnalysis of physical regularities of the gravity-cap illary-fluctuation wave motion in a plane finite thick ness layer of a viscous conducting liquid is important for many technical and technological applications [1][2][3]. A large number of earlier publications have been devoted to the capillary-gravity flow in layers of a vis cous liquid [4][5][6][7], but the entire spectrum of the wave motion has not been covered. Nevertheless, it is well known [1-3] that in the short wavelength range (shorter that 10 nm [4]), it is the forces of fluctuation origin that are responsible for the generation of waves with the same dispersion relation as gravity waves [1,3]. Fluctuation forces appear near the surface of solids (solid bottom or solid wall) at distances of ~100 nm and cause a change in the physicochemical properties of liquids [2,[8][9][10]. The structures of the flows (regu larities of the distribution of the vortex and potential components of the velocity field over the layer thick ness) associated with the periodic wave motion of the free surface of the finite thickness layer of a viscous fluid was considered in [6]. It was found that the veloc ity field of the liquid flow associated with the capil lary-gravity wave propagating over the free surface of a layer of a viscous liquid on a solid bottom has a com plex structure. In this case, the vortex flow is concen trated in a small neighborhood of the free surface and in a small neighborhood of the bottom, while the potential flow fills the entire volume of the liquid. If the wavelength is much larger than the thickness of the liquid layer, the vortex flow generated by the surface wave fills the entire volume of the liquid, and the intensity of the vortex flow at the solid bottom may considerably exceed the flow intensity at the free sur face of the liquid. If, however, the layer thickness is much larger than the wavelength, the vortex flow is concentrated at the free surface, and its intensity at the bottom tends to zero. This circumstance can be inter preted as the statement that the surface wave "does not feel the bottom."The structure of the flows associated with the peri odic wave motion at the interface of two immiscible liquids was considered in [7]. It was found that the vor tex flow is concentrated in small neighborhoods of the interface on both its sides in layers with a thickness on the order of tenths of the wavelength (depending on the viscosity of the liquid). It also turned out that the curls of the velocity fields suffer a discontinuity in the vicinity of the interface upon a transition through it. The structure of the gravity-capillary-fluctuation wave motion must obey the same regularities. It differs from the capillary-gravity wave motion only in that the capillary wave motion as such, with a typical dis persion relation ω ∝ kω ∝ k 3/2 , is limited by the motion with the dispersion relation ω ∝ (ω is the wave fre quency and k is its wavenumber) both on the side of long waves and on the side of short waves [1,3,11].The features of the wa...