  We investigate the nonradial oscillations of newly born neutron stars (NSs)
and strange quark stars (SQSs). This is done with the relativistic nuclear
field theory with hyperon degrees of freedom employed to describe the equation
of state for the stellar matter in NSs, and with both the MIT bag model and the
Nambu--Jona-Lasinio model adopted to construct the configurations of the SQSs.
We find that the gravitational-mode ($g$-mode) eigenfrequencies of newly born
SQSs are about one order of magnitude lower than those of NSs, which is
independent of models implemented to describe the equation of state for the
strange quark matter. Meanwhile the eigenfrequencies of the other modes of
nonradial oscillations, e.g., fundamental ($f$)- and pressure ($p$)-modes, are
much larger than those of the $g$-mode. In the light of the first direct
observation of gravitational waves, it is promising to employ the gravitational
waves to identify the QCD phase transition in high density strong interaction
matter.
