In this paper we present two evolved stars, HD 32887 and HD 81797, which show multi-periodic oscillations. We observed the oscillations by means of the precise radial velocity technique with the simultaneous calibration method. The high-resolution spectra of each star have been obtained with FEROS at the 2.2 m-MPG/ESO telescope in La Silla Observatory, Chile. We found variation in the stellar radial velocities and spectral line profiles. The periods of the oscillations are from several hours up to few days. The sources of the short-term oscillations of HD 32887 and HD 81797 are obviously due to stellar pulsations, which are similar to solar-like oscillations. In particular, in HD 81797 we found a clear correlation between the variation in the asymmetry of the spectral line profile, measured in the bisector velocity spans, and the radial velocity. Both stars have bisector velocity spans which also show oscillations. The periods of the bisector oscillations are similar to those of the radial velocity variation. The detection of the multi-periodic oscillations in HD 32887 and HD 81797 makes these star to be amenable targets for asteroseismology, in particular, of stars in the red giant branch.