We presented the first photometric and orbital period investigations for two near-contact binaries: HT Lyn and IR Lyn. The light-curves solutions derived from both our ground-based and various surveys’ observations, suggested that HT Lyn and IR Lyn are two semi-detached-type near-contact binaries with the secondary and primary components filling its Roche lobe, respectively. Combining the eclipse timings derived from several surveys’ data and our observations with those reported in the literature, we modified the orbital periods and revealed that their orbital periods were stable for the last two decades. The absolute physical parameters were well determined by using the empirical relations and the Gaia-distance-based method. Similar to other near-contact binaries, the primary components of HT Lyn and IR Lyn are evolving at the main-sequence stage, while their less-massive secondary components show the over-sized and over-luminosity features and should be more evolved than their primary ones. Combining the stable orbital period with the semi-detached configurations, we infer that the two near-contact binaries may be just located in the critical phase and evolving from the current semi-detached phase to the detached or contact one.

We presented the first photometric and orbital period investigations for four W Ursae Majoris-type binaries: V473 And, V805 And, LQ Com, and EG CVn. The photometric solutions suggested that V805 And and LQ Com are two total-eclipse contact binaries, while V473 And and EG CVn are partial-eclipse ones. V473 And and LQ Com belong to the A-subtype contact binaries, while V805 And and EG CVn belong to the W subtype. The O’Connell effects found in the light curves of V805 And, LQ Com, and EG CVn can be interpreted as a result of a cool spot on the surface of their less massive and hotter primary components. Based on two different methods, the absolute physical parameters were properly determined. Combining the eclipse timings derived from our observations and survey’s data with those collected from literature, we investigated their orbital period variations. The results show that the orbital periods of V473 And, V805 And, and EG CVn are undergoing a secular decrease/increase superposed a periodic variation, while LQ Com exhibits a possible cyclic period variation with a small amplitude. The secular period changes are caused mainly by the mass transfer between two components, while the cyclic period oscillations may be interpreted as the results of either the light-time effect due to the third body or the cyclic magnetic activity. Finally, we made a statistical investigation for nearly 200 contact binaries with reliable physical parameters. The statistical results suggested that the W-subtype systems are more evolved than the A-subtype ones. Furthermore, the evolutionary direction of A-subtype into W-subtype systems is also discussed. The opposite evolutionary direction seems to be unlikely because it requires an increase of the total mass, the orbital angular momentum, and the temperature differences between two components of a binary system.