This paper applies the BDF-GMRES methods for solving the Differential Algebraic Equations (DAEs) associated to the simulation of short and long-term dynamics in power systems. The investigations are concentrated on the construction of a fine ILU-GMRES preconditioner for solving efficiently not only the well-conditioned coefficient matrices but specially the ill-ones. It is shown that, if the image matrix (preconditioner origin) is firstly preprocessed (scaled, normalized and reordered), a high quality ILU preconditioner is achieved. Numerical experiments considering different test-systems and different operation conditions illustrate how tricky can be the simulation of power system dynamics if the Jacobian matrix (coefficient matrix) is ill-conditioned, normally associated to an adverse operation condition. It is shown that a traditional implicit integration method may fail in this case, whereas the combination BDF-GMRES presents an outstanding performance. © 2012 Elsevier Ltd. All rights reserved.