This article deals with the problem of eecient insurance contracts under symmetric information and non Expected Utility in innnite dimension. We consider both the case of risk and the case of uncertainty. In the case of risk, we obtain two main results: The rst one is that if the insurer is risk neutral, then for a large class of utility functions that need not be quasi-concave, eecient insurance contracts give complete coverage over a deductible. The second one is that if the insurer and the insured are both strictly strongly risk averse, then, even if there are other contingencies, eecient contracts depend only on the loss and are non decreasing, 1-lipschitz functions of the loss. Existence of eecient contracts thus follows without quasi-concavity hypotheses on utility functions. In the case of uncertainty, we rst consider C.E.U maximizers with common capacity and concave utility index and show that the set of optimal contracts is the same as in the expected utility case. We then consider agents with epsilon-contaminated capacities of the same probability and concave utility index. We show that an optimal contract is such that for small losses, it is as if it was the optimal contract for expected utility maximizers with same utility index while for high losses, it is a contract which give complete coverage over a deductible. We have beneeted from stimulating conversations with A. Chateauneuf and D. Schmeidler.