We present the results of an investigation of EUV coronal structures in 1996-2000 using the Solar and Heliospheric Observatory EIT data in 171, 195, 284, and 304 Angstrom lines. During this period, poleward- and equatorward-migrating waves of solar activity have been found in axisymmetrical distributions of EUV intensity in all four lines. In the axisymmetrical distribution of the ratio of 195 Angstrom to 171 Angstrom intensities, which is a proxy of coronal temperature from 1 x 10(6) to 2 x 10(6) K, the polar branches are less prominent. The high-latitude activity waves are caused by giant coronal magnetic loops connecting the polar magnetic field (formed during the preceding solar cycle) with the magnetic field of the "following" parts of active regions that emerged during the rising phase of the current cycle. We suggest that these coronal loops play an important role in the topological evolution of the magnetic structure of the Sun during the solar cycle.