  Cesaro convergence of spherical averages is proven for measure-preserving
actions of Markov semigroups and groups. Convergence in the mean is established
for functions in $L^p$, $1\le p<\infty$, and pointwise convergence for
functions in $L^\infty$. In particular, for measure-preserving actions of word
hyperbolic groups (in the sense of Gromov) we obtain Cesaro convergence of
spherical averages with respect to any symmetric set of generators.
