We present the near–infrared (H–band: λ = 1.65 μm) κ–space (κ1 ∝ log M, κ2 ∝ log Ie, κ3 ∝ log M/L) of high surface–brightness early and late type galaxies, based on a sample of 419 objects optically selected in regions of the A262, Cancer, and Virgo clusters and of the Coma Supercluster. We discuss the distribution of the pressure–supported and rotationally–supported systems within this space and the ensuing scaling relations. We analyze the link between galaxy structure and star formation history through a comparison of the loci occupied by galaxies of the Local Universe in both the near–infrared (this work) and optical κ–spaces. Our results support scenarios of galaxy formation and evolution with the following fundamental ingredients: collapsing proto–galactic systems are characterized by i) a bimodal distribution in mass and angular momentum; and by ii) a mass–dependent characteristic star formation time scale.