The extraordinary solar activity of October--November 2003 manifested itself in many powerful eruptive events, including large coronal mass ejections (CMEs) and extremely powerful flares. A number of major events were accompanied by practically all known phenomena of the solar activity, both local and large-scale, and caused severe space weather disturbances. We study large-scale posteruptive activity manifestations on the Sun associated with CMEs, i.e., dimmings and coronal waves, observed with extreme-ultraviolet telescopes, the SPIRIT on the CORONAS-F spacecraft and the EIT on the SOHO. During that period, observations with a cadence of 15 to 45 min were carried out by the SPIRIT in the 175 ¿ and 304 ¿ bands simultaneously. The EIT observed with 12-min cadence in the 195 ¿ band as well as with 6-hour cadence in the 171, 284, and 304 ¿ bands. These data complement each other both in the temporal and spectral coverage. Our analysis reveals that largest-scale dimmings covered almost the whole southern part of the Sun's visible side and exhibited homology, with one homological structure being changed to another configuration on 28 October. These structures show connections between large superactive and smaller regions that constituted a huge activity complex responsible for the extraordinary solar activity of that period. Coronal waves were observed at 175 ¿ as well as at 195 ¿ in some events, in areas where there were no active regions, but in the 175 ¿ images they look fainter. They were not accompanied by deep, long-living dimmings. By contrast, such dimmings were observed in active regions, in their vicinity, and between them. These facts rule out the direct relation of the phenomena of long-term dimmings and coronal waves. On 18 November, a motion of an ejecta was observed at the solar disk as a propagation of a dark feature only in the 304 ¿ band, which can be interpreted as an absorption in a cloud formed from material of the eruptive filament, which probably failed to become a CME core.