By using complex amplitude envelope representation and complex analytic signal r epresentation, propagation expressions of Lorentz pulsed beams are derived. Prop agation properties of them with different bandwidths are illustrated by numerica l calculations. It is found that they are the same in the neighbourhood of z _axis for narrowband pulses, but in the case of broadband pulses, singularities emerge near z_axis for pulsed beams obtained by using complex amplitude enve lope representation and only complex analytic signal representation is applicabl e. The conditions to decide what representation should be chosen to study pulsed beams are given. And the origin that results in the emergence of singularity is given.