Clusters of galaxies are the largest gravitationally bound systems, with three components contributing to their total mass: the dark matter (the dominant one), the hot X-ray emitting gas (the dominant baryonic component), and the optically luminous stars in galaxies. Determining the distribution of these three components and their correlations represents a key problem in modern cosmology.
A possible approach is offered by studying the relations between those global
cluster properties that can be more or less directly and easily measured,
such as the velocity dispersion 
, the total luminosity
L, and the effective radius 
.
Correlations between intrinsic parameters have effectively
been found for galaxy clusters,
as for instance between richness and velocity dispersion
(Danese et al. 1980;
Cole 1989), and between radius and luminosity
(West et al. 1989).
However these relations have a high dispersion.
Schaeffer, et al. (1993, hereafter SMCB)
analysed a sample of 19 clusters for which
luminosities, radii (West et al. 1989) and velocity dispersions
(Struble & Rood 1991) were available.
In addition to the radius-luminosity relation found by West et al. (1989),
, SMCB have also defined a
luminosity-velocity dispersion relation,
(much better than
the old richness-velocity dispersion relation).
By analogy with elliptical galaxies, for which the above three parameters
can be combined in one relation (Dressler et al. 1987;
Djorgovski & Davis 1987) defining the so-called "fundamental plane'',
and given that virialized systems should show a relation
between mass, radius and velocity dispersion,
SMCB have minimized the relation 
, and
found a best fit with a considerably lower dispersion than the
one-independent parameter relations.
The parameters 
and 
have
values similar to those measured for the fundamental plane of
elliptical galaxies.
The number of clusters for which the three parameters L, R and 
are reliably measured is however small.
Therefore we have started an observational program to increase
the cluster database, a necessary condition for further studies of the
Cluster Fundamental Plane. We present in this paper the results of
our spectroscopic observations of a sample of nearby clusters
(redshifts of member galaxies and preliminary estimates of velocity
dispersions).