Using a complex analytical signal representation,the free-space propagation properties of ultrashort pulsed Bessel-Gauss beams whose waist width is independent of frequency are studied.It is found that within the diffraction-free range the transversal intensity distribution of ultrashort pulsed Bessel-Gauss beams remains nearly unchanged,and the on-axis temporal pulse forms broaden along the propagation.Beyond this range,there is a remarkable spreading of the transversal intensity.With the increase of the propagation distance,the on-axis blue shift increases firstly,then gradually decreases after reaching its maximum,and finally approaches an asymptotic value.For example,for a single-cycle ultrashort pulsed Bessel-Gauss beam,the on-axis blue shift increases and reaches a maximum value of 0.50 fs-1,then decreases gradually,and finally approaches an asymptotic value of 0.16 fs-1 in the far field.