Abstract
The Möbius geometry of R 3 has an isotropic counterpart in R 3 ++0 . We describe the isotropic Möbius model of surfaces in R 3 ++0 and show how the degree of a surface changes under i-M inversions while the number of families of i-M circles remain constant. This gives us a generalization of the classification of families of lines and i-M circles on quadratic surfaces in R 3 ++0 to isotropic cyclides with real singularities, containing up to 4 such families