RECENT high-resolution optical observations1,2 show that the nucleus of the nearby spiral galaxy M33 has a small core radius and an unusually low velocity dispersion. These parameters yield a central dynamical timescale of only a few tens of millions of years, suggesting that the nucleus of M33 has undergone core collapse, as is believed to occur in globular clusters. Here we propose a model for the post-collapse core of M33. By analogy with globular clusters, the formation of tight binary systems powers the re-expansion of the core, and we expect in particular that low-mass X-ray binaries form with a rate about equal to that of all galactic globular clusters combined. About a dozen such binaries should be present, and their combined emission may explain the large (1039 erg s-1) and enigmatic unresolved X-ray emission from the nucleus of M33. In addition, tidal formation of cataclysmic binaries may lead to a nova rate of ≳ 1 per century. Numerous blue stragglers have probably formed through mergers caused by stellar collisions, but their density is probably too low to explain the blue colour of the nucleus. Young stars are the likely cause for the colour, and their presence may complicate the simple dynamical picture presented here.