The stability characteristics of a laboratory-scale lean premixed combustor operating on natural gas - hydrogen fuel mixtures have been studied in a variable length combustor facility. The fuel and air were mixed upstream of the choked inlet to the combustor to eliminate equivalence ratio fluctuations and thereby ensure that the dominant instability driving mechanism was flame-vortex interaction. The inlet velocity, inlet temperature, equivalence ratio and percent hydrogen in the fuel were systematically varied, and at each operating condition the combustor pressure fluctuations were measured as a function of the combustor length. The results are presented in the form of two-dimensional stability maps, which are plots of the normalized rms pressure fluctuation versus the equivalence ratio and the combustor length, for a given inlet temperature, inlet velocity, and fuel mixture. In order to understand the effects of operating conditions and fuel composition on the observed stability characteristics, two-dimensional chemiluminescence images of the flame structure were recorded at all operating conditions and for all fuel mixtures under stable conditions. Changes in the stable flame structure, as characterized by the location of the flame's "center of heat release", were found to be consistent with the observed instability characteristics. The location of the flame's "center of heat release" was found to lie along a single path for all operating conditions and fuel mixtures. It was also observed that there were regions of stable and unstable combustion as one moved along this path. Furthermore it was found that flames having the same "center of heat release" location, but different operating conditions and fuel composition, have very nearly the same flame shape. These results will be useful for developing phenomenological models for predicting unstable combustion.