We report here the additive Runge-Kutta methods for computing reactive Euler equations with a stiff source term, and in particular, their applications in gaseous detonation simulations. The source term in gaseous detonation is stiff due to the presence of wide range of time scales during thermal-chemical non-equilibrium reactive processes and some of these time scales are much smaller than that of hydrodynamic flow. The high order, L-stable, additive Runge-Kutta methods proposed in this paper resolved the stiff source term into the stiff part and non-stiff part, in which the stiff part was solved implicitly while the non-stiff part was handled explicitly. The proposed method was successfully applied to simulating the gaseous detonation in a stoichiometric H2/O2 /Ar mixture based on a detailed elementary chemical reaction model comprised of 9 species and 19 elementary reactions. The results showed that the stiffly accurate additive Runge-Kutta methods can capture the discontinuity well, and describe the detonation complex wave configurations accurately such as the triple wave structure and cellular pattern. We report here the additive Runge-Kutta methods for computing reactive Euler equations with a stiff source term, and in particular, their applications in gaseous detonation simulations. The source term in gaseous detonation is stiff due to the presence of wide range of time scales during thermal-chemical non-equilibrium reactive processes and some of these time scales are much smaller than that of hydrodynamic flow. The high order, L-stable, additive Runge-Kutta methods proposed in this paper resolved the stiff source term into the stiff part and non-stiff part, in which the stiff part was solved implicitly while the non-stiff part was handled explicitly. The proposed method was successfully applied to simulating the gaseous detonation in a stoichiometric H2 / O2 / Ar mixture based on a detailed elementary chemical reaction model comprised of 9 species and 19 elementary reactions. The results showed that the stiff exactly additive Runge-Kutta methods can capture the discontinuity well, and describe the detonation complex wave configurations accurately such as the triple wave structure and cellular pattern.