We report on the discovery of Griffiths-like phase in several compounds of the R 5 ͑Si x Ge 1−x ͒ 4 ͑R = Gd, Tb, Dy, and Ho͒ system, through the existence of an anomalous behavior on the reciprocal magnetic susceptibility ͑ −1 ͒. We found that this anomaly is restricted to the samples which present the Gd 5 Si 2 Ge 2 -type ͑monoclinic͒ or the Sm 5 Ge 4 -type ͕orthorhombic-II ͓O͑II͔͖͒ structural phases at room temperature. This peculiar effect originates from local disorder within the crystallographic structure, stabilized and enhanced by the competing intralayer and interlayer magnetic interactions. From this strong competition, a ratio of ϳ0.5 between Néel and the Griffiths-like temperatures is always found in the O͑II͒ structure. In addition, a universal ͑x , T͒ phase diagram is proposed with an interpretation based on percolative processes.