  We investigate the dynamical state of superclusters in Lambda cold dark
matter ($\Lambda$CDM) cosmological models, where the density parameter
$\Omega_0=0.2-0.4$ and $\sigma_8$ (the rms fluctuation on the $8h^{-1}$Mpc
scale) is $0.7-0.9$. To study the nonlinear regime, we use N-body simulations.
We define superclusters as maxima of the density field smoothed on the scale
$R=10h^{-1}$Mpc. Smaller superclusters defined by the density field smoothed on
the scale $R=5h^{-1}$Mpc are also investigated. We find the relations between
the radially averaged peculiar velocity and the density contrast in the
superclusters for different cosmological models. These relations can be used to
estimate the dynamical state of a supercluster on the basis of its density
contrast. In the simulations studied, all the superclusters defined with the
$10h^{-1}$Mpc smoothing are expanding by the present epoch. Only a small
fraction of the superclusters defined with $R=5h^{-1}$Mpc has already reached
their turnaround radius and these superclusters have started to collapse. In
the model with $\Omega_0=0.3$ and $\sigma_8=0.9$, the number density of objects
which have started to collapse is $5 \times 10^{-6}h^3$Mpc$^{-3}$. The results
for superclusters in the N-body simulations are compared with the spherical
collapse model. We find that the radial peculiar velocities in N-body
simulations are systematically smaller than those predicted by the spherical
collapse model ($\sim 25$% for the $R=5h^{-1}$Mpc superclusters).
