The stability of two superposed buoyancy vortices is studied linearly in a two-level SQG 1 model. The basic state is chosen as two top-hat vortices (with uniform buoyancy), coaxial and with same radius. Only the vertical distance between the two levels and the top and bottom buoyancy intensities are varied, the other parameters are fixed. The linear perturbation equations around this basic state form a two-dimensional ODE for which the normal and singular mode solutions are numerically computed. For normal modes, the system is stable if the vortices are sufficiently far from the other to prevent vertical interactions of the buoyancy patches, or if they are close to each other but with very different intensities, again preventing the resonance of Rossby waves around their contours. The vortex is unstable if the intensities are similar and if the vortices are close to each other vertically. The growth rates of the normal modes increase with the angular wave-number, also corresponding to shorter vertical distances. The growth rates of the singular modes do not depend much on the bottom buoyancy at short time, but, as expected, they converge towards the growth rates of the normal modes. This study remaining linear does not predict the final evolution of such unstable vortices. This nonlinear evolution will be studied in a sequel of this work.