We report on time-resolved optical spectroscopy of ten non-eclipsing nova-like cataclysmic variables in the orbital period range between 3 and 4 hours. The main objective of this long-term programme is to search for the characteristic SWSextantis behaviour and to eventually quantify the impact of the SWSex phenomenon on nova-likes at the upper boundary of the orbital period gap. Of the ten systems so far observed, HL Aqr, BO Cet, AH Men, V380 Oph, AH Pic, and LN UMa are identified as new members of the SW Sex class. We present improved orbital period measurements for HL Aqr (Porb = 3.254 ± 0.001h) and V380 Oph (Porb = 3.69857 ±0.00002h). BO Cet and V380 Oph exhibit emission-line flaring with periodicities of 20 min and 47 min, respectively. The Hα line of HL Aqr shows significant blueshifted absorption modulated at the orbital period. Similarly to the emission S-wave of the high-inclination SW Sex stars, this absorption S-wave has its maximum blue velocity at orbital phase ∼ 0.5. We estimate an orbital inclination for HL Aqr in the range 19 ◦ < i < 27 ◦ , which is much lower than that of the emissiondominated
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