The mechanism for low-temperature photoluminescence (PL) emissions in GaNAs epilayers and GaAs/GaNxAs1 - x quantum well (QW) structures grown by molecular-beam epitaxy is studied in detail, employing PL, PL excitation, and time-resolved PL spectroscopies. It is shown that even though quantum confinement causes a strong blueshift of the GaNAs PL emission, its major characteristic properties are identical in both QW structures and epilayers. Based on the analysis of the PL line shape, its dependence on the excitation power and measurement temperature, as well as transient data, the PL emission is concluded to be caused by a recombination of excitons trapped by potential fluctuations in GaNAs.