Based on the discussion of the applicability of the local approximation, the local stability of accretion disks with adveetion is studied together with the considerations of radial viscous force and thermal diffUsion. For a geometrically thin, radiative cooling dominated disk, the thermal diffusion has nearly no effects on the thermal and viscous modes, which are both stable if the disk is also optically thick, and gas pressure dominated and are both unstable if the disk is either optically thick, radiation pressure dominated, or optically thin. The including of thermal diffusion, however, tends to stabilize the acoustic modes, which, if without advection, are unstable if the disk is optically thick, radiation pressure dominated, or optically thin, and which are stable if the disk is optically thick and gas pressure dominated. The including of very little advection has significant effects on two acoustic modes, which are no longer complex conjugates of each other. Independent of the optical depth, the instability of the outward propagating mode (O-mode) is enhanced, and that of the inward propagating mode (I-mode) is damped if the disk is gas pressure dominated, while the instability of the O-mode is damped and that of the I-mode is enhanced if the disk is radiation pressure dominated. For a geometrically slim, adveetion-dominated disk, both the thermal and viscous modes, as well as the I-mode, are always stable if the disk is optically thin. The including of thermal diffusion tends to make these modes more stable. However, the O-mode can become unstable when q/mis very large (q is the ratio of adveetive to viscous dissipated energy and mis the Maeh number), even if the thermal diffusion is considered. On the other hand, if the adveetiondominated disk is optically thick, we found there are no self-consistent acoustic modes in our local analyses. The thermal diffusion has no effect on the stable viscous mode but has a significant contribution to enhance the thermal instability.