The advent of low temperature nuclear orientation facilities operating fully on-line to accelerators/isotope separators has made a wide range of nuclei far from stability accessible for study. Conventional low temperature nuclear orientation is limited to nuclei with half-lives ≥≈ 1 hour, but with the on-line technique this limitation is reduced by several orders of magnitude, and nuclei with half-lives of seconds have successfully been oriented. In cases where the half-life is comparable with the relaxation time, attenuation of the full thermal equilibrium effect will occur, and a detailed description of the relaxation mechanism is necessary. Quantitative methods to deal with such cases are outlined, with particular emphasis given to on-line situations. Examples of the use of these methods is also given.