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 8 h ^ { -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 = 10 h ^ { -1 } Mpc .
Smaller superclusters defined by the density field smoothed on the scale R = 5 h ^ { -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 10 h ^ { -1 } Mpc smoothing are expanding by the present epoch .
Only a small fraction of the superclusters defined with R = 5 h ^ { -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 = 5 h ^ { -1 } Mpc superclusters ) .