To fulfill the requirements of the industry, the feasibility of a transportable neutron spectrometer is under study by our collaboration. Preliminary studies have led to a solution based on a unique-multi-detectors-Bonner sphere, which has the advantage to simultaneously perform many neutrons-measurements through thermal neutron detectors placed at different depths inside a polyethylene sphere. The incident neutron energy is then reconstructed using unfolding methods. The optimization of the layout of the detectors in the sphere and of the diameter of the sphere was performed thanks to GEANT4 simulations, coupled to unfolding methods such as least-squares, maximum of entropy or maximum of likelihood. Different unfolding methods have been tested. For the time being, the best unfolding results were obtained by the computer codes M.A.X.E.D. and G.R.A.V.E.L., formalized by the Nuclear Energy Agency (N.E.A.). A "personal" method based on the maximum of entropy coupled to the maximum of likelihood gives good results as well, but a few convergence parameters have still to be optimized. In the present paper, a solution of a multi-detectors-Bonner sphere is presented as well as results of unfolded neutron energy spectra. The results obtained show a good agreement with unmoderated and moderated Am/Be and 252 Cf spectra.