When polycrystalline pure Ag specimens are compressed to 40 pet and annealed, there is no noticeable texture in the recrystallized structure, and normal or abnormal grain growth occurs during annealing. When annealed further in low vacuum (10(-3) to 10(-4) Torr) after the completion of recrystallization, normal grain growth occurs at 920 degreesC and 800 degreesC, but abnormal grain growth (AGG) occurs at 700 degreesC, 600 degreesC, and 500 degreesC. When annealed in O-2 atmosphere, normal grain growth occurs at 920 degreesC and AGG at 800 degreesC, 700 degreesC, 600 degreesC, and 500 degreesC. At temperatures close to the melting point (960.5 degreesC), the grain boundaries are expected to be rough at atomic scales and hence have nearly isotropic boundary energy. The normal growth of the grains with such atomically rough boundary structures is consistent with some theoretical analysis and simulation. At low temperatures, the grain boundaries can be faceted with probably singular structures. Because these grain boundaries apparently migrate by the movement of boundary steps, AGG occurs. The observations with optical microscopy indeed indicate that some,grain boundaries are faceted at low temperatures and all of them are smoothly curved indicating anatomically rough structure at high temperatures close to the melting point. Although the results are not conclusive, they support the hypothesis that AGG occurs because the faceted singular grain boundaries migrate by the step mechanism.