  We include the tidal instability due to the 3:1 resonance in the disc
instability model developed by Hameury et al. (1998) and modified by
Buat-Menard et al. (2001). We confirm earlier results by Osaki (1989) that the
tidal instability can account for the SU UMa light curves. We show that in
ultra-low mass ratio systems such as ER UMa stars and WZ Sge stars, the
superoutburst ends while the disc is still eccentric, as proposed by Hellier
(2001). However, since the disc shrinks rapidly once a cooling wave has
started, the eccentricity should stop shortly after the end of a superoutburst.
This result disagrees with the suggestion by Hellier that decoupling the
thermal and tidal instability in the TTI model can account for late superhumps
and echo outbursts in ultra-low mass ratio systems. We propose instead that ER
UMa short supercycles can be explained either by the alternation of narrow and
wide outbursts similar to those occurring in SS Cyg, or by the effects of
irradiation (Hameury et al. 2000). In both cases, we predict that superhumps
should be permanent, which is suggested by observations (Gao et al. 1999). We
can also reproduce light curves similar to those of EG Cnc, varying the mass
transfer rate in a TTI model including both irradiation and the presence of an
inner hole in the disc.
