ASAS J105115-6032.1 (hereafter ASAS J1051) and GDS J1056047-604149 (hereafter GDS J1056) are two short-period contact binaries close to each other in the Antarctica sky area. By analyzing the light curves from AST3-1, the first photometric solutions are presented using the Wilson-Devinney (W-D) method. It is detected that both systems are W-type contact binaries with mass ratios of q = 3.2621(0.0083) and q = 4.843(0.014), respectively. Both of them have a moderate degree of contact factor of I = 46.9(1.2)% and I = 43.9(1.2)%. The asymmetries in the light curve of the intermediate-contact system GDS J1056 (strong O'Connell effect) are interpreted by a dark spot on the more massive component. For the first time, we carried out the O - C diagram analysis based on many photometric data. The results indicate an orbital period increase at a rate of dP/dt = +5.28 x 10(-7)d.- for ASAS J10511. As for GDS J1056, a period decrease of dP/dt = -5.41 x 10(-7) d.yr(-1), superimposed with a cyclic period change with a semi-amplitude of 0.00744 d and a period of 11.97 yr, is discovered. The cyclic period change may be caused by the light travel-time effect via the presence of a tertiary companion with a lowest mass of M-3 = 0.35(0.03)M-circle dot. The period increase in ASAS J1051 can be explained by the mass transfer from the less massive component to its companion. In contrast, the period decrease in GDS J1056 reveals an opposite direction of mass transfer. The facts suggest that these two intermediate-contact binaries will evolve into shallow-and deep-contact binary systems.