It is believed that most giant elliptical galaxies possess nuclear black holes with masses in excess of 10 8 M⊙. Bondi accretion from the interstellar medium might then be expected to produce quasar-like luminosities from the nuclei of even quiescent elliptical galaxies. It is a puzzle that such luminosities are not observed. Motivated by this problem, Fabian & Rees have recently suggested that the final stages of accretion in these objects occurs in an advection-dominated mode with a correspondingly small radiative efficiency. Despite possessing a long-known active nucleus and dynamical evidence for a black hole, the low radiative and kinetic luminosities of the core of M87 provide the best illustration of this problem. We examine an advection-dominated model for the nucleus of M87 and show that accretion at the Bondi rate is compatible with the best known estimates for the core flux from radio through to X-ray wavelengths. The success of this model prompts us to propose that FR-I radio galaxies and quiescent elliptical galaxies accrete in an advection dominated mode whereas FR-II type radio-loud nuclei possess radiatively efficient thin accretion disks.