  The first results of numerical analysis of classical r-modes of {\it rapidly}
rotating compressible stellar models are reported. The full set of linear
perturbation equations of rotating stars in Newtonian gravity are numerically
solved without the slow rotation approximation. A critical curve of
gravitational wave emission induced instability which restricts the rotational
frequencies of hot young neutron stars is obtained. Taking the standard cooling
mechanisms of neutron stars into account, we also show the `evolutionary
curves' along which neutron stars are supposed to evolve as cooling and
spinning-down proceed. Rotational frequencies of $1.4M_{\odot}$ stars suffering
from this instability decrease to around 100Hz when the standard cooling
mechanism of neutron stars is employed. This result confirms the results of
other authors who adopted the slow rotation approximation.
