Abstract:We trace back the past flight path of nearby neutron stars (within few kpc and up to few Myr) in order to find their birth places in supernovae in OB associations. Since the radial velocities of neutron stars are in most cases unknown, we do some calculations (and Monte Carlo simulations), to test all possibilities. Hence, the results are somewhat probabilistic. To ensure a certain birth place in a supernova, runaway stars can help: if a known runaway star is located simultaneously at the same place of a neutron star, then they were probably both ejected by a supernova in a binary system. Hence, we also trace back runaway stars. Once such binary supernovae are found, we also take spectra of the runaway (candidate) stars to search for supernova debris material in their atmospheres. This would be a final confirmation of the scenario. Thereby, we can determine the kinematic ages of neutron stars, which can be more precise than characteristic ages, so that we can test neutron stars cooling curves. One can also find supernova sites with runaway stars (with supernova debris) alone, without neutron stars, if their age or birth association is well known. Each supernova can have triggered star formation in another nearby cloud, so that we can later reconstruct the star formation history in our local environment.