A coil system generating a vertical radio-frequency (rf) field gradient (gradient) has been built for surrounding, in a horizontal magnet, a vertical sample (object) of axial symmetry. The system comprises three coaxial loops with an overall shape either spherical or ellipsoidal. The geometry has been theoretically and experimentally devised for producing a very uniform gradient (cancellation of derivatives from second order up to sixth order) in the central region where a vertical receiver/transmitter coil is installed. The latter is of the saddle-shaped type and is geometrically and electrically decoupled from the gradient coil system. This receiver/transmitter coil not only ensures an optimal signal reception but, in addition, is able to deliver perfectly homogeneous rf hard pulses which are mandatory in most NMR experiments. In its present design, the system delivers a uniform gradient in a limited region but could be extended at will. Its main advantages over static field gradients (gradients) appear clearly in the case of very short transverse relaxation times. This property has been emphasized in the case of experiments leading to the measurement of diffusion coefficients. Also, this system would be suitable for chemical shift imaging (CSI) experiments as confirmed by a preliminary test experiment.