  We study Wilson loops in N=4 SYM theory which are non-constant in the scalar
(S5) directions and open string solutions associated with them in the context
of AdS/CFT correspondence. An interplay between Minkowskian and Euclidean
pictures turns out to be non-trivial for time-dependent Wilson loops. We find
that in the S5-rotating case there appears to be no direct open-string duals
for the Minkowskian Wilson loops, and their expectation values should be
obtained by analytic continuation from the Euclidean-space results. In the
Euclidean case, we determine the dependence of the ``quark - anti-quark''
potential on the rotation parameter, both at weak coupling (i.e. in the 1-loop
perturbative SYM theory) and at strong coupling (i.e. in the classical string
theory in AdS5 x S5).
