The evolution of a magnetic field line in two dimensions near a neutral sheet is analysed. It is found that the general features of this evolution are rather independent of any particular model, provided that the magnetic field is small and the current density does not vanish. The time of arrival of a field line to the neutral sheet as well as its breaking and reconnection are proved to be finite and to satisfy a simple formula whose main parameter is the resistivity, which may be a spatial function. The shape of the evolving field lines satisfies a differential equation whose solution in some simple cases is shown to agree with certain classical reconnection configurations. Hyperresistivity is found to be more often a hindrance than a positive contribution to the reconnection process.