The family of hydrogenated fullerene C60 presents another example of a large community of fullerene polyderivatives where every member is not subjected to sterical obstacles, so that the family can potentially span the complete series from C60H2 to C60H60, at least computationally. This circumstance suggests an attractive possibility of an exhausted comparative examination of two families, C60H2k and C60F2k,at the computational level, thus disclosing the ability of the computational synthesis of fullerene derivatives to the greatest extent, as well as revealing the similarities and differences in the families’ behavior.