  This is the second paper in the series of papers dedicated to the study of
natural cluster structures in the rings of regular functions on simple complex
Lie groups and Poisson-Lie structures compatible with these cluster structures.
According to our main conjecture, each class in the Belavin-Drinfeld
classification of Poisson-Lie structures on $\G$ corresponds to a cluster
structure in $\O(\G)$. We have shown before that this conjecture holds for any
$\G$ in the case of the standard Poisson-Lie structure and for all
Belavin-Drinfeld classes in $SL_n$, $n<5$. In this paper we establish it for
the Cremmer-Gervais Poisson-Lie structure on $SL_n$, which is the least similar
to the standard one.
