Ag-Si alloys of various compositions were produced by laser-induced melting and quenching of vapour-deposited thin films. Despite cooling rates approaching 1010K/s the procedure fails to yield glassy phases for all compositions except those around 80 at.-% Si. This behaviour contrasts with that of the Au-Si system which under similar experimental conditions yields glasses at almost arbitrary concentrations. The difference in glass forming ability of these two systems, which have similar phase diagrams, is explained in terms of the difference in the heat of mixing of the liquid, and its consequent effect on both the thermodynamics and kinetics of these alloys.