We present a qualitative analysis of possible changes in the structure of accretion disks that occur in the transition from hot to cool disks. We suggest that an additional spiral-density wave can exist in the inner parts of the disk, where gas-dynamical perturbations are negligible. We consider the formation of this wave and its parameters. The results of a three-dimensional gas-dynamical simulation of a cool accretion disk are presented; these results confirm the possibility of the formation of a new, "precessional," spiral wave in the inner regions of a cool accretion disk. Possible observational manifestations of such a wave are discussed. (C) 2004 MAIK "Nauka/Interperiodica".