This paper is the first in a series in which we present the results of an ESO Large Program on the kinematics and internal dynamics of dwarf elliptical galaxies (dEs). We investigate the relations between the parameters that quantify the structure and internal dynamics of dEs such as the Faber_Jackson relation and the Fundamental Plane (FP). We show that the dE sequences in the various diagrams are disjunct from those traced by bright and intermediate-luminosity elliptical galaxies and bulges of spirals. It appears that semi-analytical models (SAMs) are able to reproduce the position of the dEs in those diagrams. While these findings are clearly a success for the hierarchical-merging picture of galaxy formation, they do not necessarily invalidate the alternative ``harassment scenario, which posits that dEs stem from perturbed and stripped late-type disk galaxies that entered clusters and groups of galaxies about 5 Gyr ago.
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