It is generally known that the use of high-energy electron linear accelerators (LINACs) in radiotherapy medical treatments may generate secondary neutrons, mainly via photonuclear (gamma, <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</i> ) giant dipole resonance reactions of incident photons with all the heavy materials present inside the gantry and along the beam line. A detailed knowledge (i.e., fluence energy distribution) of this parasite radiation, which is approximately isotropic and not confined within the primary LINAC beam field, would be of great interest to estimate the associated radiological risk for the patient and the working staff. It has been shown, in this study, that our recently developed passive Bonner sphere system, using pure gold activation foils as central detectors, is well adapted to measure neutron spectra at pulsed and intense mixed n-gamma fields with high-energy photon component. This system was used to characterize the neutron field around a new generation medical electron LINAC. Two measurement positions (isocenter and maze entrance) inside the treatment room of this facility, with the machine operating in Bremsstrahlung photon mode, were chosen. The obtained specific <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">198</sup> Au saturation activities were processed by means of the NUBAY unfolding code, which performs a Bayesian estimation of a parameterized spectrum, to derive the final neutron spectra. Another unfolding method (MAXED), based on the maximum entropy principle and which may depend to some extent on considered the initial guess or default spectrum, was also applied to check the robustness of the NUBAY solutions as well as to carry out a sensitivity analysis to confirm their stability and to corroborate the associated uncertainties on their output results. Also presented are the obtained integral quantities, in terms of neutron fluence and ambient dose equivalent rates normalized to the primary LINAC photon dose, together with an estimation of their associated uncertainties due to the unfolding code used.