It has been shown recently that the maximum penetration of the liquid phase in a vaporizing Diesel spray is relatively short compared to the overall jet penetration and that this maximum is reached in 2 - 4°CA after start of injection. This implies that the drops that are formed by atomization vaporize in a short characteristic time and length relative to other physical processes. This paper addresses an important question related to this observation: Are the vaporizing fuel drops disappearing because they reach a critical state? Related to this question is another: Under what conditions will vaporizing fuel drops reach a critical state in a Diesel engine? Single drops of pure component liquid hydrocarbons and their mixtures vaporizing in quiescent nitrogen or carbon dioxide gas environments with ambient pressures and temperatures at values typically found in Diesel engines are examined. Results from detailed computations of droplet vaporization indicate that the drop may reach the critical state if the ambient temperature and pressure exceed approximately twice that of the liquid species critical values. It is unlikely that such conditions will be encountered by vaporizing drops in a Diesel engine unless the drops are in the reaction zone. Results from computations of vaporizing single droplets and sprays using a multidimensional model are also presented. These computations which employ a simplified vaporization model indicate that the model appears to reproduce the criterion with adequate accuracy. Indeed, even the measured liquid penetration is reproduced if collisions, coalescence and secondary breakup are neglected in the spray model.