Context.Nearby luminous infrared galaxies (LIRGs) are often considered to be the local counterpart of the star forming galaxy (SFG) population atz > 1. Therefore, local LIRGs are ideal systems with which to perform spatially resolved studies on the physical processes that govern these objects and to validate assumptions made in high-zstudies because of a lack of sensitivity and/or spatial resolution.Aims.In this work we analyse the spatially resolved kinematics of the stellar component in the innerr < 1–2 kpc of ten nearby (meanz = 0.014) LIRGs, establishing the dynamical state of the stars and estimating their dynamical masses (M_dyn). We compare the stellar kinematics with those for different gas phases, and analyse the relative effects of using different tracers when estimating dynamical masses.Methods.We use seeing-limited SINFONIH- andK-band spectroscopy in combination with ancillary infrared (IR) imaging from various instruments (NICMOS/F160W, NACO/Ks and IRAC/3.6 μm). The stellar kinematics are extracted in both near-IR bands by fitting the continuum emission usingpPXF. The velocity maps are then modelled as rotating discs and used to extract the geometrical parameters (i.e. centre, PA, and inclination), which are compared with their photometric counterparts extracted from the near-IR images. We use the stellar and the previously extracted gas velocity and velocity dispersion maps to estimate the dynamical mass using the different tracers.Results.We find that the different gas phases have similar kinematics, whereas the stellar component is rotating with slightly lower velocities (i.e.V_*∼ 0.8V_g) but in significantly warmer orbits (i.e.σ_*∼ 2σ_g) than the gas phases, resulting in significantly lowerV/σfor the stars (i.e. ∼1.5–2) than for the gas (i.e. ∼4–6). These ratios can be understood if the stars are rotating in thick discs while the gas phases are confined in dynamically cooler (i.e. thinner) rotating discs. However, these differences do not lead to significant discrepancies between the dynamical mass estimations based on the stellar and gas kinematics. This result suggests that the gas kinematics can be used to estimateM_dynalso inz ∼ 2 SFGs, a galaxy population that shares many structural and kinematic properties with local LIRGs.