  We calculate the spin density matrix of top quark pairs for the reaction
$e^+e^-\to t\bar{t}X$ to order $\alpha_s$. As an application we show
next-to-leading order results for a variety of spin observables for the
$t\bar{t}$ system. These include the top quark and antiquark polarizations and
$t\bar{t}$ spin-spin correlations as a function of the center-of-mass energy
and of the top quark scattering angle for arbitrary longitudinal polarization
of the electron/positron beam.
