Low-frequency torsional forced oscillation tests have been performed on a fine-grained olivine polycrystal to determine shear wave dispersion and attenuation. The specimen was a dense hot-pressed San Carlos olivine aggregate with uniform grainsize of about 50 &mgr;m, <0.1 vol. % of melt and minor amount of hydroxyl (~100 ppm). Mechanical tests were conducted under 200 MPa hydrostatic pressure, low oscillation frequencies (0.01-1 Hz) and within the linear regime of strain (amplitude <5¿10-5). The specimen was first annealed at 1300 ¿C, and subsequently measured at a series of progressively lower temperatures. At 1300 ¿C evidence was obtained of marked viscoelastic relaxation: the shear modulus G is relatively low and strongly frequency-dependent and the attenuation Q-1 is high (G~33 GPa, Q-1~0.14 for 1 Hz). In the temperature range 1100--1300 ¿C, G depends strongly on temperature with |∂G/∂T| several times greater than the value measured in ultrasonic experiments at MHz frequencies. Q-1 varies with temperature and frequency as Q-1=A0[&ohgr;eE/RT>-n with activation energy for the relaxation rate E=420¿30 kJ/mol and exponent n=0.31¿0.02. The presence of thermal cracks complicates the interpretation of data obtained at temperatures below 900 ¿C. Grainsize-sensitive processes may be responsible for much of the observed viscoelastic relaxation. The strong temperature sensitivity of the shear modulus suggests much smaller thermal anomalies than are commonly inferred to be responsible for the variability of seismic wave speeds in the upper mantle.¿ 1997 American Geophysical Union