​​Designing advanced combustion engines requires a better understanding of the physical and chemical processes occurring during spray combustion. In this study, the ignition characteristics of conventional diesel and palm biodiesel fuels were simulated using the two-stage Lagrangian (TSL) simulation, a zero dimensional (0-D) modeling technique. For the diesel fuel surrogate, a detailed chemical kinetic model for n-heptane from LLNL (Lawrence Livermore National Laboratory), with 550 chemical species and 2450 elementary reactions was utilized. For the palm biodiesel, detailed mechanism (4800 species and 2450 elementary reactions) for the 5 basic biodiesel components; methyl palmitate, methyl stearate, methyl oleate, methyl linoleate and methyl linolenate was used. Also, simulations were performed using a reduced mechanism (115 species and 460 reactions) for surrogates of palm oil biodiesel comprising mixtures of methyl decanoate, methyl decenoate and n-heptane. The simulated data were validated against published experimental results in a constant volume combustion chamber. Validations were performed at an ambient density of 15kg/m3 and injections pressure condition of 100, 200, and 300 MPa. For both the diesel and biodiesel, the predicted ignition delay agrees with the trend obtained in the experiment at all injection pressures. The TSL model was further employed to investigate the chemical processes responsible for controlling the overall ignition under various conditions. Furthermore, the effects of exothermicity, ambient pressure, and ambient oxygen concentration on first stage ignition were studied.