The results of measurements with neutron energies up to 60 MeV are shown for the personal neutron dosemeters Thermo Electron EPD-N2, ALOKA PDM-313 and the PTB prototype dosemeter DOS-2002. All dosemeters show dose equivalent responses that are about a factor of 10, too high at 60 MeV. A new prototype dosemeter-called DOS-2005-consisting of a detector with a thin effective layer of 6 mu m has been set up at PTB. The dose equivalent response of this dosemeter and that of the newly developed dosemeter SAPHYDOSE-N was measured up to 19 MeV. Both dosemeters indicate a more flat response at high neutron energies. Further needs-optimisations, measurements and calculations-for use at high-energy accelerators and in space are discussed.