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We have studied the internal kinematics of the giant elliptical galaxy NGC 1399 in the Fornax cluster, using globular clusters (Grillmair {\it et al} 1994: ApJ 422, L9), new very deep integrated light observations at the AAT and velocities of individual planetary nebulae measured with the NTT. The various tracers cover overlapping radial zones and give the radial behaviour of the velocity dispersion out to a radius of about 24 kpc. The velocity dispersion decreases from about 360 km s$^{\rm -1}$ near the center to about 180 km s$^{\rm -1}$ at a radius of 5 kpc and then rises to about 400 km s$^{\rm -1}$ beyond 13 kpc. The integrated light observations and the planetary nebulae show that the stellar population in the outer regions of NGC 1399 is rotating rapidly: from the planetary nebulae, the rotation is about 250 km s$^{\rm -1}$ at a radius of 24 kpc. This indicates that a large amount of angular momentum resides in the outer stellar population of this giant elliptical galaxy, despite the low specific angular momentum associated with the inner regions of ellipticals, and is consistent with the angular momentum properties expected from formation by secondary infall (eg Quinn \& Zurek 1988: ApJ 331,1). In contrast, the globular cluster system of NGC 1399 shows no rotation.
