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We report the discovery and complex analyses of the first two compact hierarchical triple star systems discovered with TESS in or near its southern continuous viewing zone during Year 1. Both TICs 167692429 and 220397947 were previously unknown eclipsing binaries, and the presence of a third companion star was inferred from eclipse timing variations exhibiting signatures of strong 3rd-body perturbations and, in the first system, also from eclipse depth variations. We carried out comprehensive analyses, including the simultaneous photodynamical modelling of TESS and archival ground-based WASP lightcurves, as well as eclipse timing variation curves. Also, for the first time, we included in the simultaneous fits multiple star spectral energy distribution data and theoretical PARSEC stellar isochrones, taking into account Gaia DR2 parallaxes and cataloged metallicities. We find that both systems have twin F-star binaries and a lower mass tertiary star. In the TIC 167692429 system the inner binary is moderately inclined ($i_{mut}=27^o$) with respect to the outer orbit, and the binary vs. outer (triple) orbital periods are 10.3 vs. 331 days, respectively. The mutually inclined orbits cause a driven precession of the binary orbital plane which leads to the disappearance of binary eclipses for long intervals. In the case of TIC 220397947 the two orbital planes are more nearly aligned and the inner vs. outer orbital periods are 3.5 and 77 days, respectively. In the absence of radial velocity observations, we were unable to calculate highly accurate masses and ages for the two systems. According to stellar isochrones TIC 167692429 might be either a pre-main sequence or an older post-MS system. In the case of TIC 220397947 our solution prefers a young, pre-MS scenario.