  A self-stabilizing protocol provides by definition a tolerance to transient
failures. Recently, a new class of self-stabilizing protocols appears. These
protocols provides also a tolerance to a given number of permanent failures. In
this article, we are interested in self-stabilizing protocols that deal with
Byzantines failures. We prove that, for some problems which not allow strict
stabilization (see [Nesterenko,Arora,2002]), there exist solutions that
tolerates Byzantine faults if we define a new criteria of tolerance.
