A nuclear magnetic resonance apparatus for experiments in pulsed high magnetic fields is described. The magnetic field pulses created together with various magnet coils determine the requirements such an apparatus has to fulfill to be operated successfully in pulsed fields. Independent of the chosen coil it is desirable to operate the entire experiment at the highest possible bandwidth such that a correspondingly large temporal fraction of the magnetic field pulse can be used to probe a given sample. Our apparatus offers a bandwidth of up to 20 MHz and has been tested successfully at the Hochfeld-Magnetlabor Dresden, even in a very fast dual coil magnet that has produced a peak field of 94.2 T. Using a medium-sized single coil with a significantly slower dependence, it is possible to perform advanced multi-pulse nuclear magnetic resonance experiments. As an example we discuss a Carr-Purcell spin echo sequence at a field of 62 T.