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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.