The response of CR-39 track detectors to neutrons has been characterized and used to measure neutron yields from implosions of DD- and DT-filled targets at the OMEGA laser facility [T. R. Boehly , Opt. Commun. 133, 495 (1997)], and the scaling of neutron fluence with R (the target-to-detector distance) has been used to characterize the fluence of backscattered neutrons in the target chamber. A Monte-Carlo code was developed to predict the CR-39 efficiency for detecting DD neutrons, and it agrees well with the measurements. Neutron detection efficiencies of (1.1+/-0.2)x10(-4) and (6.0+/-0.7)x10(-5) for the DD and DT cases, respectively, were determined for standard CR-39 etch conditions. In OMEGA experiments with both DD and DT targets, the neutron fluence was observed to decrease as R-2 up to about 45 cm; at larger distances, a significant backscattered neutron component was seen. The measured backscattered component appears to be spatially uniform, and agrees with predictions of a neutron-transport code. As an additional application of the calibration results, it is shown that the neutron-induced signal in CR-39 used in charged-particle spectrometers on OMEGA can be used to determine DD and DT yields ranging from about 10(10) up to 10(14). With further improvements in the processing and analysis of CR-39, this upper limit can be increased by at least two orders of magnitude. (C) 2002 American Institute of Physics.