Asymptotic properties of low degree gravity modes and their relation to the stratification of the model through the Brunt-Väissälä frequency are discussed for a solar type model and for a 10 M⊙ model. For the solar model, taking into account the quasiadiabaticity of the solar convection zone, it is shown that two global constraints on the deep interior of the solar model can be derived from a set of g-modes periods in the observed range. However modes with large periods, i.e. larger than those up to now observed, are required to obtain informations on the stratification just below the convection zone. For the 10 M⊙ model, the preliminary results show that the existence of a layer with a large mean molecular weight gradient destroys the equidistance of the periods of gravity modes of a given degree and that some informations on the properties of this layer can be obtained from the analysis of the g-modes periods.