  In this paper we investigate, using high resolution N-body simulations, the
density profiles and the morphologies of galaxy clusters in seven models of
structure formation. We show that these properties of clusters are closely
related to the occurrence of a significant merging event in the recent past.
The seven models are: (1) the standard CDM model (SCDM) with $\Omega_0 = 1$,
$\Lambda_0=0$ and $h=0.5$; (2) a low-density flat model (FL03) with
$\Omega_0=0.3$, $\Lambda_0=0.7$ and $h=0.75$; (3) an open model (OP03) with
$\Omega_0=0.3$, $\Lambda_0=0$ and $h=0.75$; (4) a low-density flat model (FL02)
with $\Omega_0=0.2$, $\Lambda_0=0.8$ and $h=1$; (5) an open model (OP02) with
$\Omega_0=0.2$, $\Lambda_0=0$ and $h=1$; (6) a low-density flat model (FL01)
with $\Omega_0=0.1$ and $\Lambda_0=0.9$; (7) an open model (OP01) with
$\Omega_0=0.1$ and $\Lambda_0=0$. We find that the density profiles and
morphologies of clusters depend both on $\Omega_0$ and on $\Lambda_0$. For
$\Lambda_0=0$, these properties are a monotonic function of $\Omega_0$.
Clusters in OP01 have the steepest density profiles, their density contours are
the roundest and show the smallest center shifts. The other extreme case is
SCDM, where clusters show the least steep density profiles and the most
elongated contours. For a given $\Omega_0$ ($<1$), clusters in the flat model
(i.e. with $\Lambda_0=1-\Omega_0$) have flatter density profiles and less
substructures than in the corresponding open model. In particular, our results
show that low-density flat models with $\Omega_0\sim 0.3$, which are currently
considered as a successful alternative to SCDM, can produce a substantial
fraction of clusters with substructures. This is in contrast to the conception
that this kind of models may have serious problem in this aspect.
