  We propose that the abundance anomalies of proton-capture elements in
globular clusters, such as the C-N, Na-O, Mg-Al and Na-F anti-correlations,
were produced by super-massive stars with M ~ 10,000 Msun. Such stars could
form in the runaway collisions of massive stars that sank to the cluster center
as a result of dynamical friction, or via the direct monolithic collapse of the
low-metallicity gas cloud from which the cluster formed. To explain the
observed abundance anomalies, we assume that the super-massive stars had lost
significant parts of their initial masses when only a small mass fraction of
hydrogen, Delta X ~ 0.15, was transformed into helium. We speculate that the
required mass loss might be caused by the super-Eddington radiation
continuum-driven stellar wind or by the diffusive mode of the Jeans
instability.
