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.
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