Linear stability analyses for two-dimensional natural convection in horizontal air-filled annuli are performed for three-dimensional perturbations and radius ratios in the range 1.2 ≤ R ≤ 3. Flow transitions from moderate to large gap annuli, which have not been reported before, are thoroughly investigated. As a result, stability diagrams are obtained for finite and for infinite length annuli. The leading disturbances and threshold values are found to agree well with experimental data and three-dimensional numerical solutions. Three-dimensional simulations were also carried out to examine the influence on the flow stability of no-slip boundary conditions at the end walls.