This research paper presents a comprehensive analysis of RR Lep and BF Vel, two southern short-period semi-detached oscillating Algols (oEA stars), which are shown to be triple systems. Spectral types of the primary components were determined and radial velocities calculated from spectra observed with the Australian National University's 2.3m telescope andWide Field Spectrograph. Spectra of the NaI D doublet confirmed the presence of tertiary components which were apparent in the broadening function analyses and, with H{alpha} spectra during primary eclipses, indicated chromospherical activity in their secondary components. Ground-based telescopes were used for observations in several pass bands for photometric analyses. These observations were complemented by data from the Transiting Exoplanet Survey Satellite (TESS) mission to enable the modelling of the light curves, followed by a detailed analysis of pulsations. Eclipse-timing variation (ETV) analyses of both systems were used to determine the most likely mechanisms modulating the orbital period. We found mass values M1=2.9M_{sun} and M2=0.75M{sun} for the components of RR Lep, and M1=1.93M{sun} and M2=0.97M{sun}_ for those of BF Vel. By integrating information from photometry, spectroscopy and ETV analysis, we found that tertiary components revolve around both systems. The primary star of RR Lep pulsates in 36 frequencies, of which five were identified as independent modes, with the dominant one being 32.28d^-1^. The pulsating component of BF Vel oscillates in 37 frequencies, with the frequency 46.73d^-1^ revealed as the only independent mode. For both systems, many frequencies were found to be related to the orbital frequency. Their physical properties were compared with other oEA stars in Mass-Radius and Hertzsprung-Russell diagrams, and the pulsational properties of their delta Sct components were compared with currently known systems of this type within the orbital-pulsation period and log g-pulsation period diagrams.