Almost all research in the field of principal-agent-theory is done in the expected utility framework. A more general approach to decision making under risk has been provided by Machina (1982), in which the crucial independence axiom is replaced by a much weaker differentiability assumption. Risk aversion can than be described by the characteristics of a “local” utility function. This paper provides a corresponding generalization of the approach of Holmström (1979) to principal-agent-problems. First it is shown that an optimal risk allocation implies that the marginal rates of substitution, now expressed in terms of the “local” utility function, are identical for both principal and agent. In the presence of Moral Hazard, a deviation from an optimal risk allocation is necessary in order to set better incentives. A solution to this problem is derived, which contains the result of Holmström as a special case.