The authors propose a class of generalized accelerated overrelaxation (GAOR) methods for the linear complementarity problem, whose special case reduces to generalized successive overrelaxation (GSOR) methods. Some sufficient conditions for convergence of the GAOR and GSOR methods are presented when the system matrix \(M\) is an \(H\)-matrix, \(M\)-matrix and a strictly or irreducible diagonally dominant matrix. The monotone convergence of the new methods are discussed when \(M\) is an \(L\)-matrix. The numerical results show that the proposed methods are effective for large and sparse linear complementarity problems when \(M\) is an \(H\)-matrix with positive diagonals.