Mass transfer cycles in close binaries with evolved companions

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.