  We develop the a posteriori error analysis of finite element approximations
of implicit power-law-like models for viscous incompressible fluids. The Cauchy
stress and the symmetric part of the velocity gradient in the class of models
under consideration are related by a, possibly multi--valued, maximal monotone
$r$-graph, with $\frac{2d}{d+1}<r<\infty$. We establish upper and lower bounds
on the finite element residual, as well as the local stability of the error
bound. We then consider an adaptive finite element approximation of the
problem, and, under suitable assumptions, we show the weak convergence of the
adaptive algorithm to a weak solution of the boundary-value problem. The
argument is based on a variety of weak compactness techniques, including
Chacon's biting lemma and a finite element counterpart of the Acerbi--Fusco
Lipschitz truncation of Sobolev functions, introduced by L. Diening, C. Kreuzer
and E. S\"uli [Finite element approximation of steady flows of incompressible
fluids with implicit power-law-like rheology. SIAM J. Numer. Anal., 51(2),
984--1015].
