The influence of upstream fuel/air mixture stratification on the blowoff behavior of flames behind two-dimensional bluff bodies is investigated theoretically. The analysis identifies two important dimensionless groups through which stratification exerts an influence: a stratification parameter D which characterizes the severity of the stratification, and a dimensionless activation energy ECp/RΔH, which affects the ignitability of the fresh mixture. Results are presented for two possible scenarios. For the kind of stratification which might occur unintentionally in an otherwise homogeneous flow, stratification always reduces the blowoff limits of flows which are entirely lean or entirely rich, but in flows which vary from lean to rich, blowoff limits may be either reduced or improved. For the kind of stratification which might be intentionally introduced, for instance as a thin rich layer in an otherwise lean mixture, blowoff limits are always improved, often drastically.