  We investigate particle laws of motion derived from nonstandard kinetic
actions of a special form. We are guided by a phenomenological scheme--the
modified dynamics (MOND)--that imputes the mass discrepancy observed in
galactic systems to a departure from Newtonian dynamics below a certain
acceleration scale a0. In the limit a0 goes to 0 the theory goes to Newtonian
dynamics. In the opposite limit the action becomes proportional to 1/a0.
Galilei-invariant such theories must be strongly non-local; this is a blessing,
as such theories need not suffer from the illnesses that are endemic to
higher-derivative theories. We discuss the possibility that such a modified law
of motion is an effective theory resulting from the elimination of degrees of
freedom pertaining to the universe at large (the near equality a0=cH0 being a
trace of that connection). A virial relation for bounded trajectories is
derived. Exact solutions are obtained for circular orbits, which pertain to
rotation curves of disk galaxies. We also explore, in passing, theories that
depart from the conventional
  Newtonian dynamics for very low frequencies. The present formulation
contrasts, on important accounts, with earlier, modified-gravity formulations.
