Incompressible and nearly incompressible problems are treated herein with a mixed finite element formulation in order to avoid ill-conditioning that prevents accuracy in pressure estimation and lack of convergence for iterative solution algorithms. A multilevel dual domain decomposition method is then chosen as an iterative algorithm: the original FETI and FETI-DP methods are extended to deal with such problems, when the discretization of the pressure field is discontinuous throughout the elements. A dedicated augmentation of the algorithms is proposed and the different methods are compared with several preconditioners, for bidimensional test cases. The resulting approaches are both optimal and numerically scalable, and their costs are estimated with a complexity analysis.