  Two observational campaigns were carried out during the eclipses of EE Cep in
2003 and 2008/9 to verify whether the eclipsing body in the system is indeed a
dark disk and to understand the observed changes in the depth and durations of
the eclipses. Multicolour photometric data and spectroscopic observations at
both low and high resolution were collected. We numerically modelled the
variations in brightness and colour during the eclipses. We tested models with
different disk structure. We considered the possibility of disk precession. The
complete set of observational data collected during the last three eclipses are
made available to the astronomical community. Two blue maxima in the colour
indices were detected during these two eclipses, one before and one after the
photometric minimum. The first (stronger) blue maximum is simultaneous with a
"bump" that is very clear in all the UBVRI light curves. Variations in the
spectral line profiles seem to be recurrent during each cycle. NaI lines always
show at least three absorption components during the eclipse minimum and strong
absorption is superimposed on the H_alpha emission. These observations confirm
that the eclipsing object in EE Cep system is indeed a dark, dusty disk around
a low luminosity object. The primary appears to be a rapidly rotating Be star
that is strongly darkened at the equator and brightened at the poles. Some of
the conclusions of this work require verification in future studies: (i) a
complex, possibly multi-ring structure of the disk in EE Cep; (ii) our
explanation of the "bump" observed during the last two eclipses in terms of the
different times of obscuration of the hot polar regions of the Be star by the
disk; and (iii) our suggested period of the disk precession (~11-12 P_orb) and
predicted depth of about 2 mag the forthcoming eclipse in 2014.
