A local, small perturbation, linear, inviscid stability analysis is applied to co-flowing reacting shear layers downstream of a bluff body flame holder. Velocity and density profiles are taken from premixed flame experiments. Linear stability theory is employed to determine the regions of transition from absolute to convective instabilities in the wakes of transverse circular cylinder and rectangular bar stabilized flames at two fuel lean conditions, one close to blow off and the other further from blow off. Instabilities in the near wake region of the flame holders are found to be absolute in nature while further downstream in the recirculation zone, the stabilities are of the convective type. Frequencies corresponding to regions of absolute instabilities are determined and compared to previously measured experimental values known to result in vortex shedding.