  We show how the Newton-Hooke (NH) symmetries, representing a nonrelativistic
version of de-Sitter symmetries, can be enlarged by a pair of translation
vectors describing in Galilean limit the class of accelerations linear in time.
We study the Cartan-Maurer one-forms corresponding to such enlarged NH symmetry
group and by using cohomological methods we determine the general 2-parameter
(in D=2+1 4-parameter)central extension of the corresponding Lie algebra. We
derive by using nonlinear realizations method the most general group -
invariant particle dynamics depending on two (in D=2+1 on four) central charges
occurring as the Lagrangean parameters. Due to the presence of gauge
invariances we show that for the enlarged NH symmetries quasicovariant dynamics
reduces to the one following from standard NH symmetries, with one central
charge in arbitrary dimension D and with second exotic central charge in D=2+1.
