The accretion disks are usually supposed symmetric to reflection on the Z=0 plane. Asymmetries in the flow are be ver-y small in the vicinity of the compact accretor. However their existence can have a important role in the case of subkeplerian accretion flows onto black holes. These flows lead to strong heating and even to the formation of shocks close to the centrifugal barrier. Large asymmetries are due to the development of the KH instability triggered by the small turbulences at the layer separating the incoming flow from the out coming shocked flow. The consequence of this phenomenon is the production of asymmetric outflows of matter and quasi periodic oscillations of the inner disk regions up and down the Z=0 plane.

The local instabilities of accretion disks were extensively studied, with the considerations of radial advection, thermal diffusion and different disk geometry, dominated pressure and optical depth. Two inertial-acoustic modes in a geometrically thin, radiative cooling dominated disk depart from each other if very little advection is included. A geometrically slim, advection-dominated disk is found to be always stable if it is optically thin. However, if it is optically thick, the thermal diffusion has no effect on the stable viscous mode but has a significant contribution to enhance the thermal instability.