  Many globular cluster systems have a distinct bimodal metallicity
distribution function (MDF) which has strikingly similar features in many large
galaxies of all types. By using the Milky Way cluster system as a typical
example, we show that bimodal MDFs can be very well matched with a double
``accreting-box'' chemical enrichment model in which both the halo (metal-poor)
and bulge (metal-rich) clusters form during an early phase of gas inflow
simultaneously with star formation. However, differences in effective yield
between the two phases are not enough by themselves to reproduce the observed
MDF shape: gas infall is required for both phases, and either the initial gas
or the infalling gas must have very different metallicities in the two separate
phases.
