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In this paper we study a continuous-time multiparameter algebraic Riccati equa-tion (MARE) with an indefinite sign quadratic term. The existence of a unique and bounded solution of the MARE is newly established. We show that the Kleinman algorithm can be used to solve the sign indefinite MARE. The proof of the conver-gence and the existence of the unique solution of the Kleinman algorithm is done by using the Newton–Kantorovich theorem. Furthermore, we present new algorithms for solving the generalized multiparameter algebraic Lyapunov equation (GMALE) by means of the fixed-point algorithm. 2002 Elsevier Science (USA) 1