  The AdS/CFT correspondence predicts a phase transition in Wilson loop
correlators in the strong coupling N=4, D=4 SYM theory which arises due to
instability of the classical string stretched between the loops. We study this
transition in detail by solving equations of motion for the string in the
particular case of two circular Wilson loops. The transition is argued to be
smoothened at finite `t Hooft coupling by fluctuations of the string world
sheet and to be promoted to a sharp crossover. Some general comments about
Wilson loop correlators in gauge theories are made.
