A structure model for the Ge(111)-(4 x 4)-Ag surface is proposed. The model was derived by applying direct methods to surface X-ray diffraction data. It is a missing top layer reconstruction with six Ag atoms placed on Ge substitutional sites in one triangular subunit of the surface unit cell. A ring-like assembly containing nine Ge atoms is found in the other triangular subunit. The stability of the ring assembly may be due to Ge-Ge double bond formation. Trimers of Ge atoms, similar to the trimers found on the Ge(111)-(root 3 x root 3)R30 degrees-Ag surface, are placed in the corners of the unit cell. (C) 1998 Elsevier Science B.V. All rights reserved.