The report deals with a two-stroke diesel engines, which are started by compressed air and where fuel is not injected in cylinders during starting process. Only when speed of crankshaft rotation is sufficient to ensure ignition of fuel in cylinders the starting air supply is interrupted and the fuel is injected in cylinders. The differential equation of the first revolution of crankshaft motion was done, and offered a very simple numerical integration scheme. By way of example calculations are carried out for a particular engine as in case where compressed air is supplied to all cylinders as well as the compressed air is delivered only to half of the cylinders.