A description is given of pulsed gradient spin echo (PGSE) NMR experiments in which large pulsed magnetic field gradients may be required. The design contraints are discussed and, in particular, the problem of the use of large pulsed magnetic field gradients in conjunction with large polarizing fields is considered. Issues addressed concern probe mechanical assembly, current supply requirements, and pulse shape design. We describe a quadrupolar coil with a gradient amplitude of 1.65 T m-1 A-1 which has been used successfully up to a maximum gradient of around 40 T m-1. A diffusion coefficent of 7.5 x 10-16 m2 s-1 has been measured using this system, the lowest yet achieved by PGSE NMR methods.