  We analyse the optical spectral properties of the complete sample of Very
Luminous Infrared Galaxies presented by Wu et al. (1998a,b) and we find a high
fraction (~50 %) of spectra showing both a strong H_delta line in absorption
and relatively modest [OII] emission (e(a) spectra). The e(a) signature has
been proposed as an efficient method to identify dusty starburst galaxies and
we study the star formation activity and the nature of these galaxies, as well
as the effects of dust on their observed properties. We examine their emission
line characteristics, in particular their [OII]/H_alpha ratio, and we find this
to be greatly affected by reddening. A search for AGN spectral signatures
reveals that the e(a)'s are typically HII/LINER galaxies. We compare the star
formation rates derived from the FIR luminosities with the estimates based on
the H_alpha line and find that the values obtained from the optical emission
lines are a factor of 10-70 (H_alpha) and 20-140 ([OII]) lower than the FIR
estimates (50-300 M_sun yr^-1). We then study the morphological properties of
the e(a) galaxies, looking for a near companion or signs of a
merger/interaction. In order to explore the evolution of the e(a) population,
we present an overview of the available observations of e(a)'s in different
environments both at low and high redshift. Finally, we discuss the role of
dust in determining the e(a) spectral properties and we propose a scenario of
selective obscuration in which the extinction decreases with the stellar age.
