  We analyze adaptive mesh-refining algorithms in the frame of boundary element
methods (BEM) and the coupling of finite elements and boundary elements
(FEM-BEM). Adaptivity is driven by the two-level error estimator proposed by
Ernst P. Stephan, Norbert Heuer, and coworkers in the frame of BEM and FEM-BEM
or by the residual error estimator introduced by Birgit Faermann for BEM for
weakly-singular integral equations. We prove that in either case the usual
adaptive algorithm drives the associated error estimator to zero. Emphasis is
put on the fact that the error estimators considered are {not even globally
equivalent to weighted-residual error estimators for which recently convergence
with quasi-optimal algebraic rates has been derived.
