The viscoelasticity of mildly impure polycrystalline iron has been studied over the temperature range 20--1300 ¿C through a combination of seismic-frequency torsional forced oscillation and microcreep tests. For all temperatures above ~400 ¿C, linear absorption band behavior is observed, both strain energy dissipation Q-1 and shear modulus dispersion providing evidence of substantial departures from ideal elastic behavior. For 3 s oscillation period the temperature sensitivity of the shear modulus |∂G/∂T| averages 0.04 GPa K-1. An even larger derivative applies to the highest temperatures within the bcc field (600--800 ¿C) and at longer periods. The isothermal variation of Q-1 with period T0 is generally adequately described by Q-1~T0α. Within the bcc field the exponent α, and hence the distribution D(&tgr;)~&tgr;α-1 of relaxation times, are temperature-independent, allowing the parameterization Q-1~0 exp(-E/RT)>α, with α=0.20¿0.02 and activation energy E=280¿30 kJ mol-1. Within the fcc field, the exponent α increases systematically with increasing temperature from ~0.1 to ~0.3 across a wide temperature interval, indicating that the distribution of relaxation times within the absorption band is strongly temperature-dependent. Steady-state viscosities inferred mainly from microcreep records for temperatures between 1000 and 1300 ¿C, lie within the range (0.2-2)¿1013 Pa s. The observed mix of recoverable anelastic and viscous behavior (the latter becoming progressively more important with increasing temperature and time/period) is tentatively attributed to diffusional processes operative at grain boundaries in the relatively fine-grained bcc-Fe and to processes involving dislocations in the coarser-grained specimens of the fcc phase. Relaxation of internal stresses caused by pronounced single-crystal elastic anisotropy probably dominates the anelastic response of both phases. The marked elastic anisotropy of fcc-Fe makes it an attractive alternative to the hcp structure widely favored for the dominant crystalline phase of the Earth's inner core. At seismic frequencies and homologous temperatures approaching unity in the inner core, solid-state viscoelastic relaxation probably accounts for much of the observed seismic wave attenuation and contributes through the associated dispersion to the unusually high value of Poisson's ratio. ¿ 2000 American Geophysical Union