Background: Radiotherapy with Antiprotons is currently investigated by the AD-4/ACE collaboration. The hypothesis is that the additional energy released from the antiprotons annihilating at the target nuclei can enable a reduced dose in the entry channel of the primary beam. Furthermore an enhanced relative biological effect (RBE) has already been beam measured in spread out Bragg peaks of antiprotons, relative to that found in the plateau region. However, the antiproton annihilation process is associated with a substantial release of secondary particles which contribute to the dose outside the volume targeted for irradiation. A major part of this peripheral dose arise from neutrons, which in particular are problematic due to their high RBE for secondary cancer incidence. We have measured the fast and thermal neutron spectrum in different geometrical configurations in order to experimentally quantify the neutron contribution to the dose found outside the primary beam. Materials and methods: The AD-4/ACE collaboration has access to an antiproton beam at CERN. All results acquired here are obtained with a pristine 47 MeV antiproton beam. Neutron bubble detectors were used for measuring the neutron spectrum. Additionally, we used a cylindrical polystyrene loaded with several pairs of thermoluminescent detectors containing Lithium-6 and Lithium-7, which effectively detects thermalized neutrons. The obtained results are compared with FLUKA imulations. Results: The results obtained with the neutron bubble detectors are problematic since these detectors also respond well towards charged particles such as protons and pions. Taking this into account we find 12 µSv dose equivalent (NCRP 38) for 107 antiprotons at a distance of 8 cm from the annihilation vertex. The TLD measurements at 7 cm from the annihilation vertex inside the polystyrene phantom produced a response which corresponds to a neutron fluence of 8000 neutrons/cm2 per 107 antiprotons. This is equivalent to a neutron kerma of 1.4e-9 Gy (adult brain) per 107 antiprotons following ICRU 46. Conclusion: The thermalized part of the neutron spectrum is very low, and does not pose a problem for radiation therapy. However, the contribution from fast neutrons is much more significant. The dose equivalent contribution from neutrons originate from the patient alone and reaches levels which are found in passive moderated proton therapy. The exact consequence of this is depending on the outcome of the ongoing discussion of the risk from secondary cancer from neutrons.