The Numerical Action Method is a fully nonlinear approach to the reconstruction of the dynamical history of the local universe. I will present detailed results from recent large-scale N-body tests which will help to clarify the strengths and weaknesses of the method. In particular, I will investigate the recovery of the individual orbit histories of some 500 dark matter haloes interacting in a region of radius 26 Mpc/h, or about the scale of the local supercluster, using only the halo redshfits, angular positions, and masses at the present epoch. I will show that the method can accurately recover halo distances and peculiar velocities in most cases, while the quality of the reconstructions suffers the most in highly non-linear regions.