The composition and structure of metallic meteorites accord with a mechanism of their formation by slow cooling from elevated temperatures under conditions of high pressure. These conditions produced the Widmanstatten pattern in 6–13 per cent Ni-Fe compositions. At some time in their history and at a temperature not higher than 300–400°C this pressure was suddenly changed, accompanied perhaps by a temperature rise followed by comparatively rapid cooling. Approximate times necessary to form the Widmanstätten pattern at several temperatures are calculated. These are estimated from diffusion rates in nickel-iron alloys and from the time of heating required at high temperatures to erase the Widmanstatten pattern (twenty or more hours at 1000°C). From the calculated values it is concluded that within the age of the solar system (3 × 10 9 years) equilibrium could not have been achieved below 300–400°C. In octahedrites, average observed composition of taenite (gamma phase, 30 per cent Ni) and of kamacite (alpha phase, 6 per cent Ni) is evidence according to the phase-diagram of equilibrium at a temperature of 500°C. Nevertheless, taenite variable in composition from edge to centre indicates final stages of Widmanstätten figure formation at a lower temperature range where restricted diffusion prevented homogeneity within the time available. This discrepancy is reconciled by effects of high pressure which lower the gamma-alpha transformation temperatures and the corresponding temperatures for Widmanstatten figure formation. If the prevailing lower equilibrium temperature was about 300°C, the necessary pressure is calculated to be about 10 5 atmospheres. Pressures of this magnitude suggest conditions in the interior of a planetary body. Pressure also accounts for absence of Widmanstätten patterns in meteorites containing more than about 12–13 per cent Ni. These alloys (nickel-rich ataxites) remained for the majority of their extraterrestrial existence in the gamma state. Subsequent fragmentation into smaller bodies released pressure and the alloys either transformed simultaneously into metastable α 2phase, or cooled relatively rapidly through the transformation temperature, forming a mixture of alpha and gamma phases. Meteorites containing more than about 27 per cent Ni contain all taenite which accords with laboratory experience showing that 34 or more per cent Ni-Fe alloys resist transformation under all conditions of cooling or heat treatment. Sudden release of pressure, as by changing distortional stresses or fragmentation of the parent body, accounts in major part for the metallographic structure called plessite. Reduction of pressure momentarily transplants gamma alloy to the alpha-gamma region of the phase diagram resulting in transformation to metastable α 2phase which is an acicular or martensite-like transformation product analogous to structures produced in similar laboratory alloys by thermal quench. Heating of α 2phase within the alpha-gamma region (or slow cooling from this region after transformation) results in a mixture of finely divided alpha and gamma phases either unresolved or granular as observed under the microscope. These products correspond to unresolvable, fine and coarse plessite. Acicular kamacite observed in some meteorites is also explained by sudden transformation occurring through pressure changes. Rapid cooling is not an equivalent explanation, because most original meteorite masses were too large to cool at the required rapid rate.