We investigated the development of the spherically symmetric dust-like cloud at the linear and nonlinear stages of its evolution in ΛCDM models of the Universe with nonzero 3-space curvature. The conditions of development at an arbitrary redshift z ≥ 0 are expressed through the following linear values of amplitudes: the amplitude δ_min of perturbation, whose expansion will be stopped at time infinity, the amplitude δ_ta of perturbation, whose expansion will be stopped at the given moment of time, and the amplitude δ_c of perturbation, which has been collapsed at the given moment of time. Their dependencies on cosmological model parameters and redshift are obtained. The ratios of nonlinear values to linear ones of amplitudes D^r_nl/D_l and the characteristic sizes k_nl/k of perturbation are expressed through the approximate dependence on linear value of the amplitude d_z.