In this work, an experimental study and kinetic characterization of the combustion process and a morphologic study of hydrogen/methane−air mixtures are presented. The experimental study was performed in an optical access cylindrical constant-volume combustion bomb. This bomb is equipped to register the instantaneous pressure during combustion and records the combustion images using the high-speed Schlieren optical technique. This provides straightforward information to compute the flame propagation speed and direct evidence of the apparition of cellularity on the flame front. Through the images of the combustion process, it is possible to conduct a morphological study of the process using a flame monitoring model. Simultaneously, by means of a two-zone thermodynamical model, with the temporal evolution of pressure as the main intake, significant parameters are determined during the combustion process of different fuels under premixed conditions: burning velocity, rate of combustion, burned and unburned temperature, burned mass fraction, and rate of heat release, among others. Experimental results are compared with kinetic modeling results obtained with the Cantera package using the Gri-Mech 3.0 kinetic mechanism. Results show that a greater percentage of hydrogen in the fuel mixture increases the burning velocity and the cellularity of the flame front surface. At the same time, leaner mixtures and higher equivalence ratios enhance the apparition of the cellularity onset in the flames. Burning velocity increases with the increase in the initial temperature and the fuel/air mixture equivalence ratio. All the results obtained were validated with other data from the literature.