The structural properties of a sample of 50 dEs in the Virgo cluster are here derived from Near InfraRed (NIR, H-band 1.65 $\mu$m) surface photometry and analysed. One-dimensional surface brightness (SB) profiles are extracted using elliptical isophote fitting. They are characterised by means of structural parameters, namely the half light radius $R_e$, the average surface brightness within $R_e$ ($\mu_e$), and a concentration index ($c_{31}$). We show that typical dEs have close-to-exponential NIR SB distributions.

The relations between dEs and giant ellipticals (Es) are investigated by comparing the NIR structural parameters of 273 Es in nearby clusters. Further analysis is conducted using the optical-NIR colour $B-H$ and by studying the relationships between structural and dynamical parameters (fundamental plane) for the two classes of galaxies. The transition between the two regimes is smooth and no dichotomy is seen.