We have computed the cross section for tt production by gluon-gluon fusion at next-toleading order (NLO) in the QCD coupling, keeping the full dependence on the tt spins. Furthermore we have determined to the same order the spin dependent cross sections for the processes g+q(q)→tt+q(q). Together with our previous results [1] for q+q→tt(g) these results allow for predictions, at NLO QCD, of the hadronic production of tt pairs in a general spin configuration. As an application we have determined the degree of correlation of the t and t spins at NLO, using various spin quantisation axes.