  We investigate the strongly correlated ion dynamics and the degree of
coupling achievable in the evolution of freely expanding ultracold neutral
plasmas. We demonstrate that the ionic Coulomb coupling parameter $\Gamma_{\rm
i}$ increases considerably in later stages of the expansion, reaching the
strongly coupled regime despite the well-known initial drop of $\Gamma_{\rm i}$
to order unity due to disorder-induced heating. Furthermore, we formulate a
suitable measure of correlation and show th at $\Gamma_{\rm i}$ calculated from
the ionic temperature and density reflects the degree of order in the system if
it is sufficiently close to a quasisteady state. At later times, however, the
expansion of the plasma cloud becomes faster than the relaxation of
correlations, and the system does not reach thermodynamic equilibrium anymore.
