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.