  Nonrelativistic conformal groups, indexed by l=N/2, are analyzed. Under the
assumption that the "mass" parametrizing the central extension is nonvanishing
the coadjoint orbits are classified and described in terms of convenient
variables. It is shown that the corresponding dynamical system describes,
within Ostrogradski framework, the nonrelativistic particle obeying (N+1)-th
order equation of motion. As a special case, the Schroedinger group and the
standard Newton equations are obtained for N=1 (l=1/2).
