  For four newly suggested microscopic equations of state of neutron star
matter, we construct equilibrium sequences of rapidly rotating neutron stars in
general relativity. The sequences are the normal and supramassive evolutionary
sequences of constant rest mass. We find that for these equations of state the
maximum (gravitational) mass rotating models occur (in central density and
rotation rate $\Omega$) before the maximum--$\Omega$ models. We calculate
equilibrium sequences for a constant value of $\Omega$ corresponding to the
most rapidly rotating pulsar PSR 1937+21. Also calculated is the radius of the
marginally stable orbit and its dependence on $\Omega$.
