  In the present paper, we examine a Crouzeix-Raviart approximation for
non-linear partial differential equations having a $(p,\delta)$-structure for
some $p\in (1,\infty)$ and $\delta\ge 0$. We establish a priori error
estimates, which are optimal for all $p\in (1,\infty)$ and $\delta\ge 0$,
medius error estimates, i.e., best-approximation results, and a primal-dual a
posteriori error estimate, which is both reliable and efficient. The
theoretical findings are supported by numerical experiments.
