Deformation experiments on two fine-grained anhydrite aggregates have revealed two high-temperature flow regimes: (1) twinning and dislocation creep at high stresses (&sgr;), and (2) diffusion creep accompanied by grain boundary sliding at low stresses. Each regime is characterized by a power law constitutive equation, diagnostic microstructures, and crystallographic preferred orientations (CPO). Experiments were performed at 400¿--800 ¿C, strain rates of 10-3--10-6 s-1, and confining pressures of 150--300 MPa on natural (d=30 μm) and synthetic (d=12 μm) anhydrites. The data for both anhydrites, corrected for grain size (d), are combined into a single composite flow law. The anhydrites show strain hardening for &sgr;>150 MPa and steady state flow for &sgr;≤150 MPa. Regime 1 is characterized by a flow law with a stress exponent (n)=5. The deformation microstructures are indicative of twinning and dislocation creep: twins, undulatory extinction, grain flattening, serrate grain and twin boundaries, high dislocation densities, and newly recrystallized strain-free grains. Recrystallization occurs by grain and twin boundary migration and subgrain rotation. The CPO reflects twinning at low strains and a combination of slip systems at high strains. In regime 2 the rheology is indicative of diffusion creep with n=1. There is very little microstructural evidence of the bulk deformation. Grains are equant and have very low dislocation densities, and grain boundaries are smooth and gently curved. Split cylinder experiments reveal significant grain boundary relief attributed to grain boundary sliding. The CPO within this regime is random. The rheology and microstructures of regime 2 strongly suggest that diffusion creep accompanied by grain boundary sliding is the dominant deformation mechanism. ¿ American Geophysical Union 1995