Recently a new trend in theoretical works has appeared which claims th
at tile nonlocal effects may be relevant for the HTSC, containing high
-J(c) weak links (twin boundaries, stacking faults etc.). In such weak
links a new type of vortices - Abrikosov-Josephson (AJ) vortices - ma
y arise and move freely along the defects, leading to dissipation. In
the present work the first observation of a steep non-linear dependenc
e of the surface resistance R(s) of YBaCuO thin film and high quality
ceramic on microwave magnetic field amplitude H-omega, which is a uniq
ue feature for the dissipation due to the current-driven oscillation o
f Al-vortex, is reported. At the same time the dependence R(beta)(H-om
ega) is well described by the current-induced critical state model pro
posed by Sridhar. Additional experiments which may help to distinguish
between the two models are discussed.