A multi-step dynamical phase transition from the locked to the running stat
e of atoms in response to a de external force is studied by molecular dynam
ics simulations of the generalized Frenkel-Kontorova models in the underdam
ped limit. We show that the hierarchy of depinning transition recently repo
rted [Braun et al., Phys. Rev. Lett. 78 (1997) 1295] strongly depends on th
e friction. In the present study we consider (i) a generalized FK model wit
h highly anisotropic quasi-one-dimensional rectangular potential, and (ii)
an isotropic triangular system, where the interactions between neighboring
"channels" play an important role in the dynamics. Copyright (C) 1998 Elsev
ier Science B.V.