In this monograph the local disturbance decoupling problemwith stability istreated for nonlinear systems. Thisproblem consists in finding a (dynamic) state feedback for agiven control system with two kinds of inputs, viz.controlled inputs and (uncontrolled) disturbances such thatafter application of this feedback the outputs are notinfluenced by the disturbances and the resulting internaldynamics are locally exponentially stable. In case onlystatic state feedback is allowed two essentially differentsolutions are obtained, viz. a fundamental one and a moreproblem-oriented one. Both methods generalize well-knownsolutions for linear systems. In the last chapter a solutionis found in case dynamic state feedback is allowed. Here atypical nonlinear phenomenon is pointed out, namely thatthere exist nonlinear systems for which the disturbancedecoupling problem (with stability) can be solved byapplying dynamic feedback, but not by using static feedback.The bookis intended for researchers in mathematicalnonlinear systems theory. Geometric techniques play a keyrole in the book. Therefore, in Chapter 6 algebraictechniques are recalled and used.