This paper deals with fault detection problem for nonlinear continuous-time systems transformed to a LPV form. Adaptive set observers techniques are applied for joint state and parameter estimation in order to avoid the exponential complexity obstruction usually met in set-membership nonlinear estimation. The obtained estimates on the sets of admissible values for the parameters and the state are used for interval residuals generation. The efficacy of the proposed approach is demonstrated on a three-tank-system benchmark.