  We give a global analysis of mass transfer variations in low-mass X-ray
binaries and cataclysmic variables whose evolution is driven by the nuclear
expansion of the secondary star. We show that limit cycles caused by
irradiation of the secondary by the accreting primary are possible in a large
class of these binaries. In the high state the companion transfers a large
fraction of its envelope mass on a thermal timescale. In most cases this
implies super-Eddington transfer rates, and would thus probably lead to
common-envelope evolution and the formation of an ultrashort-period binary.
Observed systems with (sub)giant secondaries stabilize themselves against this
possibility either by being transient, or by shielding the secondary from
irradiation in some way.
