The stability of thin current sheets, such as commonly occur in space plasmas, is investigated in the presence of a magnetic normal component. The investigation is based on hybrid simulations using a suitably adapted electron pressure model. In order to properly represent the effects of the electron cyclotron motion in the magnetic normal component, we include the cyclotron part of the electron pressure evolution in an implicit manner. The results of a number of these simulations are presented with emphasis on a comparison with the linear analytical theory (Kuznetsova et al., this issue), and on the nonlinear evolution of the tearing instability. We find, in agreement with linear theory, a transition to stability for electron mass below a certain threshold, which depends on the initial configuration. The results suggest that the onset of fast substorm evolution in the magnetotail may be a two-step process, where another presently not included mechanism leads to the destabilization of the tearing instability followed by the nonlinear growth of a large scale instability. ¿ American Geophysical Union 1995