The theory of nonconservative systems close to nonlinear integrable ones is presented in this monograph. With the example of concrete quasi-conservative systems close to nonintegrable ones, the results of numerical analysis are represented, and the problem on application of the small parameter method is analyzed. The fundamental part of the monograph is devoted to the investigation of the perturbable systems. Both autonomous and nonautonomous (periodic in time) systems are considered. The global analysis of systems close to the two-dimensional Hamiltonian ones takes the central place in this...