International audienceWe discuss the generation and propagation of nondiffracting twisted pulses at microwaves, obtained through polychromatic spectral superposition of higher-order Bessel beams. The inherent vectorial structure of Maxwell's equations has been considered to generalize the nondiffracting solution of the scalar wave equation with azimuthal phase variation. Since a wide frequency bandwidth is necessary to synthesize time-limited pulses, the non-negligible wavenumber frequency dispersion, which commonly affects the propagation in the microwave range, has been taken into account. For this purpose, a higher-order Bessel beam is generated by enforcing an inward cylindrical traveling-wave distribution over a finite aperture. We pre...