THE synthesis of macroscopic quantities 1,2 of the fullerenes C60 and C70 has led to discoveries of several unusual properties 3-10, in particular the high conductivity 3 and superconductivity 4-6 of alkali-metal-doped phases. Here we report a superconducting phase of C60 doped with caesium and rubidium, which has the highest transition temperature T(c) and the largest diamagnetic shielding found so far for the alkali-metal-doped compounds. Cs(x)Rb(y)C60 (x = 2 and y = 1 in the dopant feed) exhibits a T(c) of 33 K and a diamagnetic shielding of over 60%. This is also the highest T(c) yet observed in a molecular superconductor. The variation of T(c) with dopant, T(c)(K(x)C60) [18 K] < T(c)(Rb(x)C60)[approximately 29 K] < T(c)(Cs(x)Rb(y)C60) [33 K], supports the interpretation that the transition temperature of these fullerides is determined mainly by the density of states at the Fermi level.