We report the results of X ray diffraction experiments with the diamond anvil cell to pressures above 300 GPa at room temperature on pure iron and an iron-nickel alloy. These data extend throughout the pressure range of the bulk of the outer core of the Earth and provide for the first time direct pressure-volume measurements on geophysically important materials at such conditions. Both iron and iron-nickel are observed to remain in the hexagonal close-packed structure to the maximum pressures. A combined fit to all recent compression data up to 300 GPa gives the following Birch-Murnaghan equation-of-state (EOS) parameters for iron: V ₀₂ = 6.73(1) cm³ mol⁻¹, K ₀₂ = 165(4) GPa, and K'₀₂ = 5.33(9). (Value in parentheses refers to the uncertainty of the last digit; e.g., 6.73(1) refers to 6.73 + 0.01.). Similar parameters are obtained with a recent “universal” form of the EOS of solids. For an Fe_0.8 Ni_0.2 alloy, the equation-of-state parameters are nearly identical, within error: V ₀₂ =· 6.737(5) cm³ mol⁻¹, K ₀₂ = 172(2) GPa, and K'₀₂ = 4.95(9). In terms of volume, the alloy equation-of-state is indistinguishable from that of pure iron and the densities differ (dominantly in proportion to their atomic weights) by ∼0.3 Mg m⁻³ at 330 GPa. Within the range of uncertainty in Earth model densities and trade-offs with the percentage light component in the core, nickel could be present in the core in an amount at least equal to its estimated abundance in the Earth. A direct comparison with (solid) inner core densities is now possible and places direct constraints on the thermal models of the Earth's interior.