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 deg. 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 parametrization. Also reported are the data without corrections for neutron flux attenuation in the target and other intervening materials and for neutron production in nontarget 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.