The effects of a constant cross-tail magnetic field By on the phase space structures and the observational signatures of nonlinear particle dynamics in the quiet time magnetotail are examined. The separation of phase space into dynamically distinct regions (transient, stochastic and integrable) is found to persist, albeit with considerable complications. In addition, it is shown that if |By| is less than the Bz component, the resonant coherent chaotic scattering of particles and the resulting distribution function features persist. If |By|>Bz, on the other hand, the majority of the particles are forward scattered through the current sheet, and there is no discernible signature of the resonance in the distribution function. This is significant in that the presence or absence of the resonance effect in observed distribution functions can constrain the magnitude of By. ¿ American Geophysical Union 1996