This paper describes the neutron emission observed during an investigation of the characteristics of fast linear Z-pinches using a low-inductance condenser bank. The neutron production is compared with the results obtained elsewhere and is shown to be different in several respects from that obtained with low-power banks, but is quite similar to that reported in more recent, high-power experiments. It is shown that much of the yield is non-thermonuclear, and a number of existing theories for the production of neutrons by acceleration processes in a plasma are discussed. A process of neutron production in fast linear pinches is suggested, which qualitatively accounts for many recently reported results; the proposed mechanism becomes the well-known Colgate process in discharges where m = 0 instabilities lead to narrow necks in the plasma. Reasons are given to account for the absence of appreciable thermonuclear yields which might be expected from theoretical considerations.