<p>In this work, we extended a global four-step combustion modelling approach to include the combustion of fuel blends involving hydrogen and methane. We were able to address key difficulties in the calibration process as the fuel blend ratio approached that of pure hydrogen–oxygen combustion. The first challenge involved solving the system of equations that determines the equilibrium state of the global species, while enforcing appropriate physical bounds on the solution. The second challenge was to develop a strategy to prevent endothermic reactions from occurring during the production of one of the product groups. Upon addressing these challenges, a model was developed that matched the ignition delay times and induction to reaction time ratios when compared to detailed chemistry. Moreover, the detonation velocities were recovered across the entire range of fuel blend ratios. Finally, two-dimensional simulations were carried out for stoichiometric hydrogen–oxygen, diluted with argon, and undiluted blended hydrogen–methane–oxygen. For the hydrogen–oxygen mixture, we found that the four-step combustion modelling approach was more than six times as fast to compute and captured the same cellular structure as its detailed chemistry counterpart. However, the real savings were achieved for the blended mixture, where the four-step combustion modelling approach was found to be more than forty times faster compared to using a detailed chemical mechanism that included hydrocarbon combustion. The proposed strategy thus presents a novel approach to simulate the combustion of blended fuels, where the application of detailed chemistry models may be too prohibitive.</p>