The Collisional-Radiative model CoRaM-Al is elaborated and implemented in a OD numerical approach in the purpose of describing the formation of the plasma resulting from the interaction between a tau = 4 ns Nd:YAG laser pulse and an aluminium sample in vacuum. The influence of the four harmonics at 266, 355, 532 and 1064 nm on the behavior of the nascent plasma is studied. In each case, the fluence is set equal to the threshold above which a phase explosion takes place (fluence of 7.7, 7.4, 6.8, 5.1 J cm(-2) in order of increasing wavelength). The model takes into account free electrons and excited states of Al, Al+, Al2+ and Al3+. Both groups of particles are characterized by their translation temperature in thermal non-equilibrium. Besides, each population density is assumed to be in chemical non-equilibrium and to behave freely through the involved seven elementary processes (electron impact induced excitation and ionization, elastic collisions, multiphoton ionization, inverse laser Bremsstrahlung, direct thermal Bremsstrahlung and spontaneous emission). Atoms passing from the sample to the gas are described by considering classical vaporization phenomena (governed by the Hertz-Knudsen law) so that the surface temperature is limited to values less than the critical point (T-c = 6700 K). The relative role of the elementary processes is discussed and the time-evolution of the excitation of the species is analyzed for the four considered wavelengths. This study allows to determine the different excitation temperatures as well as their evolution in time. Thus the conditions required for the achievement of the Local Thermodynamic Equilibrium can be precisely described.