By means of two-dimensional N.M.R. spectroscopy, the sixteen time-averaged magnetic dipolar couplings between proton spins of partially (non-selectively) deuteratedn-hexane oriented in a liquid crystal are determined. Using multiple-quantum N.M.R. together with simple models of the solute energy in the liquid crystalline environment, the dipole couplings are assigned to specific pairs of protons on the hexane molecule. One of the parameters of the models is the trans-gauche energy difference, for which the value consistent with the N.M.R. observations is about 3·5 kJ mol-1, higher than the usually assumed values of about 2·0 kJ mol-1. The order tensors and conformational probabilities derived from the data and models are presented and the possibility of extending these experiments to larger molecules is discussed briefly.