  The arithmetics of the frequency and of the rotation number play a
fundamental role in the study of reducibility of analytic quasi-periodic
cocycles which are sufficiently close to a constant. In this paper we show how
to generalize previous works by L.H.Eliasson which deal with the diophantine
case so as to implement a Brjuno-Russmann arithmetical condition both on the
frequency and on the rotation number. Our approach adapts the Poschel-Russmann
KAM method, which was previously used in the problem of linearization of vector
fields, to the problem of reducing cocycles.
