We present a detailed kinematic analysis of the outer halo globular cluster (GC) system of M31. Our basis for this is a set of new spectroscopic observations for 78 clusters lying at projected distances between Rproj ~20-140 kpc from the M31 centre. These are largely drawn from the recent PAndAS globular cluster catalogue; 63 of our targets have no previous velocity data. Via a Bayesian maximum likelihood analysis we find that GCs with Rproj > 30 kpc exhibit coherent rotation around the minor optical axis of M31, in the same direction as more centrally- located GCs, but with a smaller amplitude of 86+/-17 km s-1. There is also evidence that the velocity dispersion of the outer halo GC system decreases as a function of projected distance from the M31 centre, and that this relation can be well described by a power law of index ~ -0.5. The velocity dispersion profile of the outer halo GCs is quite similar to that of the halo stars, at least out to the radius up to which there is available information on the stellar kinematics. We detect and discuss various velocity correlations amongst subgroups of GCs that lie on stellar debris streams in the M31 halo. Many of these subgroups are dynamically cold, exhibiting internal velocity dispersions consistent with zero. Simple Monte Carlo experiments imply that such configurations are unlikely to form by chance, adding weight to the notion that a significant fraction of the outer halo GCs in M31 have been accreted alongside their parent dwarf galaxies. We also estimate the M31 mass within 200 kpc via the Tracer Mass Estimator, finding (1.2 - 1.6) +/- 0.2 10^{12}M_sun. This quantity is subject to additional systematic effects due to various limitations of the data, and assumptions built in into the TME. Finally, we discuss our results in the context of formation scenarios for the M31 halo.
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