Recently, Chiang's group have prepared water-soluble polyhydroxylated C-60 derivatives (Fullerenols) in fuming sulfuric acid via hydrolysis of polycyclosulfated precursors. A suggested reaction mechanism is proposed. The calculation of different isomers of C-60(OH)(6) and C-60(OH)(12) fullerenols has been carried out using the semiempirical MNDO and MM2 methods with two different approaches: (a) consideration of the geometries and thermodynamic stabilities; and (b) consideration of the cyclosulfation and hydrolysis reaction mechanisms. For (a), the double bonds in the pentagon lead to a decrease in the electron delocalization energy. Thus, the Delta H-i(o) values of fullerenol are predicted to increase for each double bond placed in the pentagon for these fullerenols. According to the Delta H-f(o) values, the most stable structures of C-60(OH)(6) and C-60(OH)(12) With externally bound hydroxyl groups have been generated, with C, and Sg symmetries respectively. The Delta H-f(o) values for these fullerenols are 503 kcal mol(-1) (C-60(OH)(6)) and 131.8 kcal mol(-1) (C-60(OH)(12)) According to the geometric structure of C-60(OH)(6) and C-6O(OH)(12) fullerenol, multi-hydroxy additions follow 1,2- or 1,4- addition to a cyclohexatriene. For (b) the most likely products in this reaction are C-60(OH)(6) (Cs) and C-60(OH)(12) (S-6), whose Delta H-f(o) values are 573 and 141.5 kcal mol(-1), respectively. These stable structures could contain exact hydroxyl group sites in C-60, and they may be helpful in the investigation of the physical properties of polymers or other groups substituted onto fullerenols (called star-like polymers).