The question of the Local Thermodynamic Equilibrium (LTE) of laser-induced plasmas is crucial regarding the Laser-Induced Breakdown Spectroscopy (LIBS) technique. The most relevant way to assess theoretically the possible departure from LTE is to develop state-to-state models of the chemical species involved. The present paper illustrates such an elaboration in the case of aluminum and tungsten. Based on this state-to-state approach, the two collisional-radiative models CoRaM-Al and CoRaM-W are elaborated. They include elementary processes under electron and heavy particle impact in thermal non-equilibrium, spontaneous emission, radiative recombination and thermal Bremsstrahlung. These models are applied to the case of ultrashort laser-induced plasmas expanding in an argon gas at different pressure, for which a relevant collisional-radiative model is also elaborated to predict the propagation of the shock wave. The laser conditions are close to those used for a typical LIBS analysis under ultrashort regime. At high argon pressure (10(5) Pa), the relaxation of the plasma takes place according to a rather low departure from LTE, as revealed by the thorough examination of the Boltzmann plots derived from the state-to-state models. This relaxation occurs at temperature higher for aluminum than for tungsten, but close to 10,000 IC from 200 ns. Conversely, at low pressure (10 Pa), the extinction of the plasma is observed at similar to 500 ns, just after a phase corresponding to significant departure from equilibrium. These results support the idea of the choice of short gate delays close to the laser pulse for the LIBS characterization of tungsten matrices in tokamak-like conditions. (C) 2016 Elsevier B.V. All rights reserved.