Quantitative structural analysis of the galaxies present in the Hawaiian Deep Fields SSA13 and SSA22 is reported. The structural parameters of the galaxies have been obtained automatically by fitting a two-component model (Sérsic r1/n bulge and exponential disc) to the surface brightness of the galaxies. The galaxies were classified on the basis of the bulge-to-total luminosity ratio (B/T). The magnitude selection criteria and the reliability of our method have been checked by using Monte Carlo simulations. A complete sample of objects up to redshift 0.8 has been achieved. Spheroidal objects (E/S0) represent ~33 per cent and spirals ~41 per cent of the total number of galaxies, while mergers and unclassified objects represent ~26 per cent. We have computed the comoving space density of the different kinds of object. In an Einstein-de Sitter universe, a decrease in the comoving density of E/S0 galaxies is observed as redshift increases (~30 per cent less at z=0.8), while for spiral galaxies a relatively quiet evolution is reported. The framework of hierarchical clustering evolution models of galaxies seems to be the most appropriate to explain our results.