It has been shown that the variation of energy flux of a transient electromagnetic field with distances, under some conditions, may obey a slowly decaying way instead of the usual inverse‐square law. In this communication we present that the pulse beams whose spectra are depicted with the Gaussian beam theory may have slowly decreasing energy flux in the paraxial region. This result contributes new signficance to both the slowly decaying wave theory and the Gaussian beam theory.