Rate effects in the Hertzian contact loading of model glass/polycarbonate and silicon/polycarbonate bilayers bonded by epoxy adhesive are examined. Glass is used because of its high susceptibility to slow crack growth, making this conventional contribution to the rate dependencies easy to distinguish. Silicon is used as a control material with effectively no slow crack growth. Abrasion damage is introduced into the undersurfaces of the brittle coating layers to provide controlled flaws for the initiation of radial cracks from flexural stresses introduced by the contact loading. Critical loads are measured as a function of loading rate. Comparative flexural strength tests on free-standing abraded specimens show a pronounced rate dependence in the glass but none in the silicon, entirely consistent with slow crack growth effects. The glass/polycarbonate bilayer critical load data show a similar trend, but with stronger loading-rate dependence, suggesting an extraneous contribution to the kinetics from the adhesive/substrate. The silicon/polycarbonate bilayer data also show a loading-rate dependence, albeit much smaller, confirming this last conclusion. Data from cyclic contact tests on the glass/polycarbonate bilayers coincide with the loading-rate data on lifetime plots, eliminating the likelihood of a mechanical component in the fatigue response. It is concluded that the adhesive/substrate contribution is viscoelastic in nature, from energy-dissipating (but noncumulative) anelastic deformation during the cyclic loading. Critical load tests on bilayers with different exposures to external water show no influence of external environment, suggesting that internal moisture is responsible for the slow crack growth in the glass-coating bilayers.