By using complex amplitude envelope representation and complex analytic signal representation, propagation expressions of Lorentz pulsed beams are derived. Propagation properties of them with different bandwidths are illustrated by numerical 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 envelope representation and only complex analytic signal representation is applicable. 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.