Abstract: In this paper, the instability of the waves along the intertropical convergence zones is studied by means of three models: the barotropic model, the equivalent barotropic model and the three dimensional model. Analytical and numerical solutions are given for the first and the second models respectively. A possible approach for the solution of the last model is suggested. The result shows that the instability is related to the shear of basic currents, the latitude and the wave length. 2ωcosφp has been shown to be a stability factor. It has been also shown that the factors neglected in simpler models may lead to increase the instability. It gives a preliminary theoretical prove for the quite well-known synoptic experience than the transformation of the kinetic energy of the basic currents to the eddy energy of the vortices may not be considered as an un-important mechanism for the initiation of typhoons.