This paper deals with fault detection for nonlinear continuous-time systems. A procedure based on interval analysis is proposed to transform the original nonlinear model into a qLPV (quasi Linear Parametric-Varying) one in a guaranteed way. The qLPV characterisation makes it possible to derive two point observers which estimate respectively the lower and the upper bounds of the state vector using cooperativity theory. A ”set-residual” guaranteed to contain the actual value is then designed. The modelling uncertainties and measurement errors are taken into account at the design stage. The proposed methodology is illustrated through numerical simulations.