S U M M A R YWe use geodetic observations of the Earth to constrain anelasticity in the Earth's mantle at periods between 12 hr and 18.6 yr. The observations include satellite laser ranging (SLR) measurements of 12 hr and 18.6 yr tides in the J 2 component of the gravity field; spacebased observations of tidal variations in the Earth's rotation rate; and optical and space-based measurements of the Chandler Wobble period and damping. These geophysical signals are mostly sensitive to the lower mantle. The results suggest the dissipative process could consist of a single absorption band that extends across seismic periods out at least as far as ∼20 yr. The results also require values of the anelastic parameter Q that are smaller than those required by seismic observations. We interpret this as evidence that Q in the lower mantle is frequency dependent. The frequency dependence suggested by the geodetic observations is reasonably consistent with laboratory measurements, though those measurements have only been done on rocks at upper mantle conditions. After fitting and removing the 18.6 yr tide from the SLR J 2 results, we find that the 1998-2002 anomaly present in the original J 2 observations is no longer a singular anomaly in the J 2 residuals, but becomes one of a series of maxima in a quasi-decadal oscillation.There is a large body of evidence suggesting that energy is dissipated when the Earth's mantle is deformed. The mechanisms responsible for this dissipation are not well understood, and are almost certain to be different in different frequency regimes and for different stress levels. The dissipation occurs almost entirely in shear energy. Dissipation of bulk energy (associated with changes in volume) appears to be negligible for most applications.The most detailed evidence of this anelastic behaviour comes from seismic data, ranging from the attenuation of 1 s body waves to the decay of seismic-free oscillations at periods of up to tens of minutes. Seismic dissipation is usually represented in terms of a quality factor, Q, defined so that during the deformation the fraction of energy lost per cycle is 2π/Q. Seismic observations show that Q in the mantle tends to decrease (i.e. the dissipation tends to increase), as the radius increases from the core-mantle boundary up through the low-velocity zone. Q then increases dramatically at the top of the low-velocity zone, at about 80 km depth. This radial dependence is illustrated in Fig. 1, using Q values from the PREM seismic earth model (Dziewonski & Anderson 1981),The seismic evidence suggests that Q is only weakly dependent on frequency across the seismic frequency band. In fact, the PREM Q estimates, like those from most other global seismic models, were derived under the assumption that Q is independent of frequency. A more general method of parametrizing the frequency dependence across the seismic band iswhere ω is the frequency, Q 0 is the value of Q at some reference seismic frequency ω 0 , and the unknown parameter α depends on the details of the physica...