The diversity of molecular structures exhibited by fullerenes(1) suggests a wide range of interesting and useful properties. Several fullerenes are now considered to be well characterized, but only minor variations in their chemical and physical properties have been observed(2). Here we show that there are in fact two distinct classes of fullerenes, with some very different chemical properties. Members of the first class, typified by C-60 and C-70, have large energy gaps between the highest occupied and lowest unoccupied molecular orbitals (HOMO and LUMO), and are soluble in many organic solvents : The second, previously unrecognized class is represented by C-74 and selected isomers of the higher fullerenes, such as that of C-80 with icosahedral symmetry : these are either free radicals or have small HOMO-LUMO gaps. Like radical metallofullerenes, they are kinetically unstable and react readily to form insoluble, polymerized solids. These intermolecular bonds can be broken by electrochemical reduction. After reducing them to soluble anions, we have been able to isolate and characterize these new fullerenes.