Phases having fluoride-related superstructures are determined in the system K 0,5− x Ln 0,5+ x F 2+2 x (0.33 < 2 x < 0.5 and Ln = Pr … Er). The composition range in which they are observed has been studied by X-ray and electron diffraction at high resolution. (i) 2 x = 0,33 ( Ln = Tb … Er, t = 1000°C). A compound K 0,33 Ln 0,67F 2,33 is observed (monoclinic system, Cm, a ≈ a F √6, b ≈ a F √2, c ≈ 3a F √2 , β = 125°). (ii) 0,33 < 2 x < 0,5 ( Ln = Gd or Eu, t = 900°C); Phase A. An incommensurate modulated structure appears, with a wave vector q = y b q (0,25 < y < 0,33). This incommensurate structure is limited by two commensurate phases with y = 0,33 (2 x ≈ 0.33, orthorhombic system, a ≈ 2 a F, b ≈ a F√2, c ≈ 3 a F√2) and y = 0,25 (2 x > 0,45, orthorhombic system, Immm, a ≈ 2 a F, b ≈ a F√2, c ≈ 4 a F√2). (iii) 0,33 < 2 x < 0,40 ( Ln = Pr … Gd, t ≈ 800°C); Phase B. A new compound is obtained (monoclinic system, Cm, C2 ou C2 m , a ≈ 2a F √3, b ≈ a F √2, c ≈ 1 2 a F √114 , β ≈ 97°).