Multiple quasi-Bessel beams are generated by transmission of sub-30-fs pulses from a Ti:sapphire laser through refractive thin-film microaxicon arrays. Time-integrated intensity distributions at several axial positions and for pulse durations of 26 and 12.5 fs reveal significant changes of contrast, envelope function, and spatial frequency spectrum in comparison with continuous wave data. Evidence is presented that strong space-time coupling results in a time-dependent interference zone.