A process allowing the removal of contaminants from an unstable oil such as those produced by thermal or catalytic cracking, wherein, in at least one step of the process, mixing of the unstable oil with a pure or impure solvent having a dipole moment greater than 2 is performed. The stabilized diesels thereby obtained exhibit interesting properties among which significant stability features and are useful in numerous applications, some of these stabilized wide range diesels are new as well as their uses.