  In this paper we consider a large sample of optically selected clusters, in
order to elucidate the physical reasons for the existence of X-ray
underluminous clusters. For this purpose we analyze the correlations of the
X-ray and optical properties of a sample of 137 spectroscopically confirmed
Abell clusters in the SDSS database. We search for the X-ray counterpart of
each cluster in the ROSAT All Sky Survey. We find that 40% of our clusters have
a marginal X-ray detection or remain undetected in X-rays. These clusters
appear too X-ray faint on average for their velocity dispersion determined
mass, i.e. they do not follow the scaling relation between X-ray luminosity and
virial mass traced by the other clusters. On the other hand, they do follow the
general scaling relation between optical luminosity and virial mass. We refer
to these clusters as the X-ray-Underluminous Abell clusters (AXU clusters, for
short) and designate as 'normal' the X-ray detected Abell systems. We examine
the distributions and properties of the galaxy populations of the normal and
the AXU clusters, separately. The AXU clusters are characterized by leptokurtic
(more centrally concentrated than a Gaussian) velocity distribution of their
member galaxies in the outskirts ($1.5 < r/r_{200} \leq 3.5$), as expected for
the systems in accretion. In addition, the AXU clusters have a higher fraction
of blue galaxies in the external region and show a marginally significant
paucity of galaxies at the center. Our results seem to support the
interpretation that the AXU clusters are systems in formation undergoing a
phase of mass accretion. Their low X-ray luminosity should be due to the still
accreting Intracluster gas or to an ongoing merging process.
