The multi-filter light curve analysis of V749 Aurigae (thereinafter V0749 Aur) is conducted for the first time. Its orbital period is improved from P = 0.409873 to 0.409890 d in this work. The photometric data from the All-Sky Automated Survey for SuperNovae (ASAS-SN) were utilized to examine the revised orbital period. Then, the phased multi-filter light curves were computed with the new period, and analyzed with the Wilson–Devinney (W-D) code. The results reveal that V0749 Aur is a marginal contact binary with a large temperature difference of about ΔT = 1600 K. It is a poor thermal contact binary, the light curves of which depart from EW-type and show EB-type light variations. Thus, V0749 Aur belongs to a particular group of binaries, named B-type binaries, predicted by the Thermal Relaxation Oscillation (TRO) theory. In addition, the amplitude differences in different bands of the light curves, imply the existence of a third light. The contribution of the third light detected by the light curve analysis is consistent with the contribution of a visual star, which is in the same line of sight as V0749 Aur but at a different distance. With its marginal contact and short period properties, V0749 Aur merits further attention as a potential transitional sample in binary evolution.

First multi-colour complete light curves and low-resolution spectra of short-period eclipsing binary TT Cet are presented. The stellar atmospheric parameters of the primary star were derived through spectra fitting as: $T_{eff}=7\,091\pm124\,{\text{K}}$ , $\log g = 4.15\pm0.33\,{\text{cm}}/\text{s}^2$ , and $[Fe/H]=-0.23\pm0.04\,\text{dex}$ . The light curves were analysed using the Wilson–Devinney code. The photometric solution suggests that this target should be a near-contact binary with the primary component filling its critical Roche lobe (i.e. SD1-type NCB). The luminosity enhancement around the primary light maximum (phase 0.10–0.40) on the light curve was detected like other SD1-type NCBs, which could be caused by a hot spot near the facing surface of the secondary component due to mass transfer. Long-term decrease of the orbital period at a rate of $dP/dt=-5.01\,({\pm}0.06)\times 10^{-8}\,{{\text{d}} \cdot{yr}}^{-1}$ was detected by the O–C analysis, which supports the mass transfer from the primary to the secondary and is consistent with its primary filling configuration. No third body was found through the light curve and O–C analysis. TT Cet may locate in the broken contact stage predicted by the thermal relaxation oscillation theory (TRO) and will evolve to the contact stage eventually. It is another good observational example supporting the TRO theory. We have collected all known SD1-type NCBs with absolute parameters from the literatures. The relations of these parameters are summarised for these rare systems.

High-precision photometric data of V505 Cyg from TESS and one spectrum observed by us are presented in this work, and the stellar atmospheric parameters of the primary component were derived via spectral fitting. Applying the Wilson–Devinney code, the photometric elements were computed for the first time. The results show V505 Cyg is a near contact binary with the primary filling its Roche Lobe and the secondary a little under-filling, along with the temperature difference of about ΔT = 1900 K between the two components. The eclipse is total and lasts for about 90 minutes, which is about 0.1 phase, so the photometric results are reliable. This system belongs to near-contact binaries with the light curves enhanced around the left shoulder of the secondary minimum, which can be explained by a hot spot on the secondary components due to mass transfer, via a stream from the primary components hitting the facing surface of the secondary components. Meanwhile, we conducted an orbital period investigation of it in detail. The orbital period study based on all times of minimum including 230 new ones determined by us reveals a secular period decreasing at the rate of dP/dt = −2.31 × 10−7 d · yr−1. The decrease of the orbital period can be the result of mass transfer between the components, agreeing well with the configuration and the asymmetric light curves of V505 Cyg. V505 Cyg is therefore another rare example of mass transferring marginal contact binary lying on the rapid evolutionary stage predicted by the Thermal Relaxation Oscillation theory. With the orbital period decrease, V505 Cyg will evolve into an overcontact binary.