Secondary neutron-production cross-sections have been measured from interactions of 290 MeV/nucleon C and 600 MeV/nucleon Ne in a target composed of simulated Martian regolith and polyethylene, and from 400 MeV/nucleon Ne interactions in wall material from the International Space Station. The data were measured between 5 and 80 deg in the laboratory. We report the double-differential cross sections, angular distributions, and total neutron-production cross sections from all three systems. The spectra from all three systems exhibit behavior previously reported in other heavy-ion, neutron production experiments; namely, a peak at forward angles near the energy corresponding to the beam velocity, with the remaining spectra generated by pre-equilibrium and equilibrium processes. The double differential cross sections are fitted with a moving-source parameterization. Also reported are the data without corrections for neutron flux attenuation in the target and other intervening materials, and for neutron production in non-target materials near the target position. These uncorrected spectra are compared with SHIELD-HIT and PHITS transport model calculations. The transport model calculations reproduce the spectral shapes well, but, on average, underestimate the magnitudes of the cross sections.