A two-dimensional computer code for the simulation of heating, vaporization, ignition, and subsequent combustion of cold droplets injected in a hot uniform gas flow is developed. The numerical simulation of the processes is performed in an axisymmetric configuration for spherical droplets with boundary fitted grid point systems. Detailed models for the relevant processes are employed; in particular, detailed chemical reaction systems are used. Both methanol droplets in hot air as well as liquid oxygen droplets in gaseous hydrogen are studied. The first chemical system is relevant in diesel engine combustion, and typical conditions at 30 bar are investigated. The liquid oxygen/hydrogen system is studied at 10 bar, and the inlet liquid oxygen (LOX) droplet temperature is cryogenic (85 K)-this condition is found in liquid rocket propulsion. The computer code accounts for physical properties in this temperature range through addition of a database for LOX/hydrogen to the commonly used NASA polynomials in the temperature range between 300 and 5000 K. For the LOX droplets in gaseous hydrogen, two neighboring droplets are also considered, and the influence of droplet spacing on ignition is investigated.