In order for new inflation (slow-roll inflation) to produce sufficient e-folds of inflation, it is necessary for the effective potential for the inflaton to be very flat near the point where slow roll begins. There are two potential problems arising from supergravity models of inflation which are addressed in this chapter. The first is that gravitons (whose density was rendered negligible by inflation) may be produced by reheating after inflation. It is necessary to arrange that the reheating temperature is such that the gravitons do not have a serious effect on the abundances of deuterium and of 3He relative to 4He abundance. The second problem (the so-called ‘Polonyr problem) results from the presence in supergravity theories of scalar fields with only gravitational strength interactions, which release the energy stored in their expectation values at very late times. The hybrid inflation idea discussed may be extended to the context of supergravity.