The characteristic time of (incompressible) resistive modes in the neighbourhood of an X-point in the absence of external forcing is found to scale, when normalized on the Alfven time, as ( epsilon mod ln epsilon mod )-1 with epsilon the ratio between the Alfven and the resistive time. In X-point configurations with oblique separatrices, the mode time-scale becomes faster as the angle between the separatrices decreases. When this angle becomes of the order of mod ln epsilon mod -1, the ( epsilon mod ln epsilon mod )-1 scaling breaks down. Similar to the case of a resonant magnetic line configuration, resistive modes can be driven unstable by the inhomogeneity of the current density.