The paper concerns important differences in the evolution of plasma column structures during the production of fusion neutrons in the first and subsequent neutron pulses, as observed for plasma-focus discharges performed with the deuterium filling. The first neutron pulse, of a more isotropic distribution, is usually produced during the formation of the first big plasmoid. The next neutron pulses can be generated by the fast deuterons moving dominantly in the downstream direction, at the instants of a disruption of the pinch constriction, when other plasmoids are formed during the constriction evolution. In both cases, the fusion neutrons are produced by a beam-target mechanism, and the acceleration of fast electron- and deuteron-beams can be interpreted by transformation and decay of the magnetic field associated with a filamentary structure of the current flow in the plasmoid.