  Recent observations of two unusual Z Cam systems, V513 Cas and IW And have
shown light curves that seem to contradict the disc-instability model for dwarf
novae: outbursts are appearing during standstills of the system when according
to the model, the disc is supposed to be in a hot quasi-equilibrium state. We
investigate what additional physical processes need to be included in the model
to reconcile it with observations of such anomalous Z Cam systems. We used our
code for modeling thermal-viscous outbursts of the accretion discs and
determined what types of mass-transfer variations reproduce the observed light
curves. Outbursts of mass transfer (with a duration of a few days, with a short
rise time and an exponential decay) from the stellar companion will account for
the observed properties of V513 Cas and IW And, provided they are followed by a
short but significant mass-transfer dip. The total mass involved in outbursts
is of the order of 10$^{23}$g. We studied the possible origins of these mass
transfer outbursts and showed that they most probably result from a giant flare
near the secondary star surface, possibly due to the absence of star spots in
the $L_1$ region.
