Linear stability of two-dimensional natural convection in air-filled horizontal annuli is numerically investigated for radius ratios in the range 1.2 less than or equal to R less than or equal to 3 and for Rayleigh numbers less than 10(4). Bifurcation diagrams are obtained for various radius ratios and the main thresholds are tracked as a function of R. A new instability mode has been highlighted which breaks the symmetry of the basic flow. This result demonstrates the need of modeling the annular gap without assuming flow symmetry. In addition to bifurcation maps drawn in the Rayleigh number-radius ratio plane, a map of possible flow patterns is also established. This map allows to foresee the number of solutions and the corresponding flow structures. (C) 2004 Elsevier Ltd. All rights reserved.