The stability of the atomic flux from effusion cells is essential for the application of molecular-beam epitaxy (MBE) to new materials systems. In particular, the possible effects of oxygen background pressure on source stability have been a concern to those applying MBE to the growth of oxides, such as the high T(c) superconductors. We have studied the effects of oxygen exposure on the sublimation of the alkaline earth elements Mg, Ca, Sr, and Ba from effusion cells, using deposition rate measurements and quadrupole mass spectrometry. Sublimation of Mg, Ca, and Sr is suppressed exponentially by oxygen with a characteristic pressure comparable to the source equilibrium vapor pressure. Ba sublimation is increased linearly by oxygen background. A surprising finding is that immediately after an exposure to oxygen, Mg, Ca, or Sr flux from an effusion cell is increased over a period of several minutes. We suggest an explanation for this phenomenon in terms of changes in the emissivity of oxide coated source material. The implication is that the stability of these sources is better at moderate oxygen pressures than at low oxygen pressures.