The development of new spectrometers that are sensitive to the directional distribution of neutrons requires new unfolding methods that can determine the distribution of the neutron fluence as a function of energy and angle. Such information is needed to compute non-isotropic dosimetric quantities (e.g. personal dose equivalent and effective dose). We describe an unfolding method that applies the maximum entropy principle to this problem. It maximises the relative entropy, defined as the information-theory entropy of the distribution of the neutron fluence relative to a distribution that encodes prior knowledge, subject to constraints imposed by the measurements. We provide examples of the applicability of the method using data from two directional spectrometers of different design that have been developed in the context of EVIDOS, a project concerning mixed neutron-photon field analysis in the nuclear industry. © Oxford University Press 2004; all rights reserved.