  We prove that for $C^{1+\theta}$, $\theta$-bunched, dynamically coherent
partially hyperbolic diffeomorphisms, the stable and unstable holonomies
between center leaves are $C^1$ and the derivative depends continuously on the
points and on the map. Also for $C^{1+\theta}$, $\theta$-bunched partially
hyperbolic diffeomorphism, the derivative cocycle restricted to the center
bundle has invariant continuous holonomies which depend continuously on the
map. This generalizes previous results by Pugh-Shub-Wilkinson, Burns-Wilkinson,
Brown, Obata, Avila-Santamaria-Viana, Marin.
