Neutrino and axion production in neutron stars occurs mainly as bremsstrahlung from nucleon-nucleon (NN) scattering. The energy radiated via neutrinos or axions is typically very small compared to other scales in the two-nucleon system. The rate of emission of such "soft" radiation is directly related to the on-shell NN amplitude, and thereby to the NN experimental data. This facilitates the model-independent calculation of the neutrino and axion radiation rates which is presented here. We find that the resultant rates are roughly a factor of four below earlier estimates based on a one-pion-exchange NN amplitude. (C) 2001 Published by Elsevier Science B,V.