Three-dimensional magnetic reconnetion is investigated by means of resistive MHD simulations on the basis of magnetotail models with various magnitudes of the average net cross-tail magnetic field component. Typical quantities such as parallel electric fields, reconnected flux and flow velocities are studied to determine the influence of increasing By values on the fast dynamical evolution of the magnetotail. We find that a cross-tail magnetic field of less than about 10% of the maximum lobe field strength, as typically observed, has little influence on the dynamic evolution. The dynamic growth becomes considerably suppressed for cross-tail field of about 25% of the lobe field strength, which is in the maximum observed. ¿American Geophysical Union 1990