Context. The discovery of pulsations in low-mass stars opens an opportunity to probe their interiors and determine their evolution by employing the tools of asteroseismology. Aims. We aim to analyse high-speed photometry of SDSS J145847.02+070754.46 and SDSS J173001.94+070600.25 and discover brightness variabilities. In order to locate these stars in the Teff - log g diagram, we fit optical spectra (SDSS) with synthetic non-magnetic spectra derived from model atmospheres. Methods. To carry out this study, we used the photometric data we obtained for these stars with the 2.15 m telescope at CASLEO, Argentina. We analysed their light curves and applied the discrete Fourier transform (FT) to determine the pulsation frequencies. Finally, we compare both stars in the Teff - log g diagram, with two known pre-white dwarfs and seven pulsating pre-ELM white dwarf stars, δ Scuti, and SX Phe stars Results. We report the discovery of pulsations in SDSS J145847.02+070754.46 and SDSS J173001.94+070600.25. We determine their effective temperature and surface gravity to be Teff = 7972 ± 200 K, log g = 4.25 ± 0.5 and Teff = 7925 ± 200 K, log g = 4.25 ± 0.5, respectively. With these parameters, these new pulsating low-mass stars can be identified with either ELM white dwarfs (with ∼0.17 MO) or more massive SX Phe stars. We identified pulsation periods of 3278.7 and 1633.9 s for SDSS J145847.02+070754.46 and a pulsation period of 3367.1 s for SDSS J173001.94+070600.25. These two new objects, together with those of Maxted et al. (2013, 2014), indicate the possible existence of a new instability domain towards the late stages of evolution of low-mass white dwarf stars, although their identification with SX Phe stars cannot be discarded.Facultad de Ciencias Astronómicas y GeofísicasInstituto Argentino de Radioastronomí
