We study the dimensionless spin parameter j ( = cJ / ( GM ^ { 2 } ) ) of uniformly rotating neutron stars and quark stars in general relativity .
We show numerically that the maximum value of the spin parameter of a neutron star rotating at the Keplerian frequency is j _ { max } \sim 0.7 for a wide class of realistic equations of state .
This upper bound is insensitive to the mass of the neutron star if the mass of the star is larger than about 1 M _ { \odot } .
On the other hand , the spin parameter of a quark star modeled by the MIT bag model can be larger than unity and does not have a universal upper bound .
Its value also depends strongly on the bag constant and the mass of the star .
Astrophysical implications of our finding will be discussed .