A peculiar effect, probably overlooked in some past laser induced fluorescence (LIF) and laser enhanced ionisation (LEI) experiments, is described. Such an effect has been observed when the temporal profile of an excimer laser-pumped, pulsed dye laser beam was analysed with a microchannel plate photomultiplier detector and a fast digitising signal analyser. Substantially different shapes were found at selected spatial locations, of 1 mm size, within the same laser beam. The overall time profile of the full size beam (similar to 6 mm) can be described by the overlapping of two limiting shapes, that is, a narrow pulse, of about 3 ns full-width-at-half-maximum (FWHM), and a much broader pulse (similar to 7 ns FWHM). The peak intensities of the limiting pulses differ in time by similar to 10 ns. In addition, it is shown that the two peaks also differ in wavelength by an amount which can be as large as the width of the atomic absorption line in the atomiser. The effect, which occurs in a random manner and is easily observed only with time resolution, is extremely sensitive to the alignment of the oscillator cavity of the dye laser. This was demonstrated experimentally by comparing the laser excitation and fluorescence waveforms of gallium and lead atoms in the inductively coupled argon plasma. The recognition of such anomalous behaviour is essential for a correct interpretation of some time-resolved fluorescence and ionisation experiments.