New high-precision CCD photometric light curves of two contact binary stars, TYC 1337-1137-1 and TYC 3836-0854-1, are displayed and analyzed by using the Wilson-Devinney (W-D) program. The light curve solutions show that both of them are low-mass ratio, deep overcontact binary systems with a mass ratio of q=0.1716±0.0010 and a high fillout factor of f=76.0±2.9% for TYC 1337-1137-1, and q=0.1900±0.0032 and f=79.4±7.9% for TYC 3836-0854-1, respectively. These results indicate that they are near the end evolutionary stage of contact binaries. The absolute parameters were calculated by using the new method of mass-radius relationship (0.238 ± 0.009 M e and 1.386 ± 0.050 M e for TYC 1337-1137-1, 0.228 ± 0.014 M e and 1.20 ± 0.07 M e for TYC 3836-0854-1, respectively). The preliminary orbital period analysis suggests that long-term period increases exist for both of them, which may be interpreted in two possible ways. A first possibility is mass transfer conservation from the less massive component to the more massive one leading to an orbital period increase. In this case, when their orbital angular momentum is less than three times the total spin angular momentum, they may evolve into a rapidly rotating single star. A second possibility is that the parabolic variation in the (O − C) diagram is only a part of a long-period cyclic change caused by a potential third body. In future, more high-precision observations of these two binaries are needed to confirm the form of orbital period changes.

New CCD photometric light curves of the short-period (P = 0.285 d) eclipsing binary RW Dor are presented. The observations were performed with the PROMPT-8 robotic telescope at CTIO in Chile between 2015 March and 2017 March. Other eclipse timings were obtained from the 2.15 m JS telescope at CASLEO, San Juan, Argentina in 2011 December. Based on a light curve analysis, it is found that RW Dor is a W-type shallow contact binary with a fill-out factor f ∼ 11% and a high mass ratio q ∼ 1.587 (1/q = 0.63), where the hotter component is the less massive one (M 1 ∼ 0.52 M and M 2 ∼ 0.82 M ). For orbital-period investigation, 15 new eclipse times and those previously published were compiled. O − C analysis with very weak evidence suggests that a long-term decrease in period with a rate of dP/dt = −9.61 × 10 −9 d yr −1 is superimposed on a cyclic variation (A 3 = 0.0054 d and P 3 = 49.9 yr). The long-term decrease can be interpreted as mass transfer from the more massive component to the less massive one, or combined with angular momentum loss via magnetic braking. In addition, the marginal contact phase, high mass ratio (1/q > 0.4), and long-term decrease in period all suggest that RW Dor is a newly formed contact binary via Case A mass transfer, and it will evolve into a deeper normal contact binary. If the cyclic change is correct, the light travel-time effect via the presence of a cool third body will be a more plausible explanation for this.