The question of whether or not solar g-modes can be detected and identified from ground observations is addressed. The limitation imposed by the Earth's atmosphere, the background solar noise spectrum at low frequencies, and a poor theoretical knowledge of these modes are mentioned. Using the best uninterrupted full disk velocity measurements obtained over the period 1984 to 1987, signals with amplitudes less than 5 cm/s are found in the g-modes spectral region. Cross-correlation and other techniques used to detect stable signals (g-modes) show negative results which allow an upper limit to their amplitudes and/or lifetimes to be defined.