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An essential step in the design of a model-based diagnosis system is to find a set of residual generators fulfilling stated fault detection and isolation requirements. To be able to find a good set, it is desirable that the method used for residual generation gives as many candidate residual generators as possible, given a model. This paper presents a novel residual generation method that enables simultaneous use of integral and derivative causality, i.e., mixed causality, and also handles equation sets corresponding to algebraic and differential loops in a systematic manner. The method relies on a formal framework for computing unknown variables according to a computation sequence. In this framework, mixed causality is utilized, and the analytical properties of the equations in the model, as well as the available tools for algebraic equation solving, are taken into account. The proposed method is applied to two models of automotive systems, a Scania diesel engine, and a hydraulic braking system. Significantly more residual generators are found with the proposed method in comparison with methods using solely integral or derivative causality.