We prove that the stable holonomies of a proper codimension 1 attractor #923;, for a C^r diffeomorphism fof a surface, are not C^{1+#952;} for #952; greater than the Hausdorff dimension of the stable leaves of f intersectedwith #923;. To prove this result we show that there are no diffeomorphisms of surfaces, with a proper codimension1 attractor, that are affine on a neighbourhood of the attractor and have affine stable holonomies on theattractor. ; We prove that the stable holonomies of a proper codimension 1 attractor Lambda, for a C-r diffeomorphism f of a surface, are not C1+theta for theta greater than the Hausdorff dimension of the stable leaves of f intersected with Lambda. To prove this result we show that there are no diffeomorphisms of surfaces, with a proper codimension 1 attractor, that are affine on a neighbourhood of the attractor and have affine stable holonomies on the attractor.