Abstract Theoretical and experimental results are presented for the case of Zeeman perturbed nuclear quadrupole resonance (NQR) using spin-3/2 nuclei with a small Zeeman interaction, γB 0, while the sample is very slowly rotated. It is found that the decay envelope for a simple two-pulse echo measurement can be strongly affected even though the sample may rotate only a few degrees or less during the course of the measurement. To lowest order the decay envelope can be described using a one dimensional function of the product of γB 0, the rotation rate, and the square of the pulse spacing. Aside from an indirect and weak dependence on the quadrupole asymmetry parameter, η, the result is independent of the NQR frequency. Identical results are expected for a stationary sample in a small rotating magnetic field. The effect seen here may be used to advantage to measure rotational motion, for example of particles in fluids, or may be an additional complication for some Zeeman perturbed NQR measurements, including some NQR detection and imaging methods.