13 out of 48 nova-likes in the 2.8-4 h orbital period range are eclipsing SW Sex stars - these are all the eclipsing cataclysmic variables (CVs) in this range. Apparently, SW Sex stars are very frequent and probably represent an important stage in CV evolution, as they densely gather just above the period gap and exhibit extremely high mass transfer rates. As the physical properties of SW Sex stars have nothing to do with their inclination, this suggests that all non- or weakly-magnetic CVs in the 2.8-4 h period range are physically similar to the SW Sex stars. Here, we present our project on the search for non-eclipsing SW Sex type stars. We perform time-resolved optical spectroscopy of all sufficiently bright old novae and nova-like CVs in the orbital period range between 2.8 and 4 h and search for characteristic SW Sex behaviour. Eventually we want to quantify the impact of the SW Sex phenomenon at the upper boundary of the orbital period gap.