This paper investigates the performance of the filtered-X LMS (FXLMS) and leaky filtered-X LMS (LFXLMS) algorithms in a nonlinear system. In addition, we derive the nonlinear filtered-X LMS algorithm (NLFXLMS), which is obtained by considering the nonlinear system function for the determination of the gradient of the cost function. We show that the fact of not using the exact gradient implies in a performance reduction of the adaptive algorithm. The adaptive algorithms are examined in the context of active noise control applications, which possess nonlinear components. Through numerical simulations we discuss the capabilities of the examined adaptive algorithms.