Beitr\"age zur Algebra und Geometrie Contributions to Algebra and Geometry Volume 35 (1994), No. 2, 239-257. Nichtisotrope Kreisschiebzykliden des Flaggenraumes I G. S. Kar\'an\'e Abstract. A flag space is a three-dimensional affine space with an absolute $\{\om,f,F\}$ , where $f$ is a line in the plane of infinity $\om$ and $F$ a point on $f$ \break (H. Brauner [1]-[3]). A cyclide is a surface of order 4 which intersects $\om$ only at $f$. In this paper we investigate all cyclides generated by translation of a circle in a not isotropic plane. We give normal forms and CAD pictures of these surfaces.