  We present the evolution path of the first core in rotating molecular cloud
core and the evolution during the second collapse phase using axisymmetric
numerical calculations. The structure and evolution of the rotating first core
is characterized by the angular momentum $J_{\rm core}$ and mass $M_{\rm
core}$, both of which increase with time by accretion from the infalling
envelope. We find the evolution path of it can be considered as a sequence of
equilibrium solutions with a constant $J_{\rm core}/M_{\rm core}^2$. Such
evolution paths are in good agreement with the results of three-dimensional
numerical simulations. The evolution paths is completely different from
spherical case. Except for extremely small rotation rate of $J_{\rm
core}/M_{\rm core}^2 < 0.015 G/(\sqrt{2} c_{\rm iso})$, the first core does not
increase in the central density beyond a certain maximum value and can not
begins the second collapse direct and grows in mass by accretion. Such a first
core has a very long time-scale and seems to suffer from a non-axisymmetric
evolution. In the usual case, we expect that the time-scale of a rotating first
core becomes several thousand years and several percent of the prestellar cores
contain a first core at least. Such a rotating first core has a small average
luminosity of $L_{\rm core} = 0.003-0.03$($\dot{M}_{\rm core}/\dot{M}_{\rm
ref}$) L$_{\odot}$.
