Hydrodynamic flame instabilities are studied in a Hele-Shaw burner. By studying the development of perturbations, starting from a 2D Bunsen flame at the top of the burner, growth rates are measured for propane and methane–air mixtures, and compared to theoretical predictions. It is found that the dispersion relation in a Hele-Shaw cell has the same dependence with wavenumber σ=k−k^2 as the one predicted in tubes. Markstein numbers relative to fresh gases are obtained for propane and methane flames and compared to the literature.