A systematic experimental study was performed to elucidate the conditions for which cellular patterns of diluted hydrogen diffusion flames near extinction were observed. The formation of cellular instabilities was studied for several burners: jet burners (axisymmetric jet and two-dimensional jet) and a novel one-dimensional burner. The fuel and oxidizer Lewis numbers and the initial mixture strength (fuel-to-oxygen concentration ratio normalized by the stoichiometric value) were identified as the key governing parameters. The formation of cellular flames occurs for low reactant Lewis numbers (less than one) and near the extinction limit. For the jet burners, the parameter space for cellularity was found to decrease with either decreasing initial mixture strength, either increasing the fuel jet velocity. For a given fuel mixture, the wavelength associated with the cellular instabilities was found to decrease with either decreasing oxygen concentration, or increasing the fuel jet velocity. To study the supression of hydrodynamic effects on the cellular instabilities, a unique burner was constructed to experimentally realize a onedimensional unstrained planar non-premixed flame, previously only considered in idealized theoretical models. The results shos that when the oxidizer diffuses against the bulk flow the propensity of cellular instabilities increases with decreasing the initial mixture strength which is in agreement with the theoretical predicitions for this type of burner as well as experimental results for jet diffusion flames.