In this paper, we report an experimental study of different dynamics taking place in a 20 m long passively mode-locked fibre ring laser in dual-wavelength operation, at 1531 nm and 1558 nm. For different polarization adjustments, self-starting mode locking is obtained, yielding different types of emission: bunches of solitons in quasi-stationary regime, a compact bunch of solitons coexisting with loose bunches of solitons, a noise-like pulse coexisting with bunches of solitons and a noise-like pulse displaying quasi-periodic fluctuations. In each regime, we extract information on the pulse dynamics from measurements of the temporal profile evolution using a 16 GHz real-time oscilloscope and, at the same time, we propose a phase-space diagram representation of the intensity versus the energy of the temporal profile of the pulses; the latter allows evidencing patterns that could not be identified using conventional measurement techniques.