<p>Multilevel methods are among the most efficient numerical techniques for solving large-scale systems of equations arising from the discretization of partial differential equations. The foundation of multilevel methods is a two-level scheme, which consists of compatible relaxation and coarse-level correction. In practice, some nonstationary or nonlinear iterative methods have been applied as coarse solvers, while there is little theoretical understanding of practical performance. This paper is devoted to the convergence analysis of two-level methods with general coarse solvers. In our scheme, the coarse-level system is solved by an inner iterative process, in which various solvers can be used, as long as the corresponding accuracy estimates are available.</p>