An axiomatization is presented for a Savage-type conditional subjective expected utility model. The axioms consist of extensions of the Herstein-Milnor [11] axioms for "measurable" utility, a generalization of an averaging condition in Bolker [4], and several structural conditions. The structural conditions are examined in some detail, and examples are given to show what happens to the numerical model when they do not hold. The numerical model expresses the utility of an act (or mixed act), given an event, as a weighted sum of the utilities of the act given events that partition the initial event, the weights being personal probabilities for the partition events conditioned on the initial event. The theory is compared to Savage's theory [18] and to a version of the theory of Luce and Krantz [14] for conditional expected utility.