We present new modal Q measurements of the 0S0 and 0S2 modes, and first modal frequencies and Q measurements of 2S1 and 0S3 modes. The high quality of the GGP (Global Geodynamics Project) superconducting gravimeters (SGs) contributes to the clear observation of seismic normal modes at frequencies lower than 1 mHz and offers a good opportunity for studying the behaviour of these modes. The interest of scientists in the gravest normal modes is due to the fact that they do contribute to a better knowledge of the density profile in the Earth, helping to constrain Earth's models. These modes have been clearly identified after some large recent events recorded with superconducting gravimeters, particularly well-suited for low-frequency investigations. The Ms = 8.1 (Mw = 8.4) Peruvian earthquake of June 2001 and the Ms = 9.0 (Mw = 9.3) Sumatra-Andaman earthquake of December 2004 provide us with individual spectra which exhibit a clear splitting of the spheroidal modes 0S2, 0S3 and 2S1, and a clear identification of each of the individual singlets, with a resolution never obtained from broad-band seismometers records. The Q quality factors have been determined from the apparent decrease of the amplitude of each singlet with time, according to a well-suited technique [Roult, G., Clévédé, E., 2000. New refinements in attenuation measurements from free-oscillation and surface-wave observations. Phys. Earth Planet. Inter. 121, 1 37]. The results are compared to the theoretical frequencies and Q quality factors computed for the PREM and 1066A models, taking into account both rotation and ellipticity effects of the Earth. The two observed datasets (frequencies and Q quality factors) exhibit a splitting on the observed values different from the predicted one. That seems to point out that some parameters as density or attenuation values used in the theoretical models do not explain the observations. A new dataset of frequencies and Q quality factors of the whole set of singlets of the gravest spheroidal modes is thus under construction. That dataset includes the five individual singlets of the 0S2 mode clearly identified on the SG records, the three singlets of the 2S1 mode recently observed for the first time by [Rosat, S., Hinderer, J., Rivera, L., 2003b. First observation of 2S1 and study of the splitting of the football mode 0S2 after the June 2001 Peru earthquake of magnitude 8.4. Geophys. Res. Lett. 30, 21211, doi:10-1029/2003L018304], the 0S0 radial mode, and the seven individual singlets of the 0S3 mode.