ABSTRACT
We call attention to a small group of cataclysmic variable stars (whose prototype might be considered RZ LMi) that have complex light curves fo similar shape which repeat with typical periods of a few weeks. The predictability of the time of each superoutburst and the stability of the shape of the light curve is unexpectedly high for cataclysmic variables, which are well-known for erratic variations in both the timing and the shape of their outbursts. The phenomenon appears to be closely related to SU Ursae Majoris-type superoutbursts, especially since superhumps appear in these stars. The similiarities and differences between these RZ LMi stars and SU UMa systems are summerized and discussed in the context of extant models for the superoutbursts of SU UMa-type dwarf novae.