The quasi-two-dimensional system of coupled Frenkel-Kontorova chains (so-called x-chains, which are classical harmonic chains of atoms in a periodic substrate potential) is considered. The authors study the case when each x-chain has a kink (x-kink) that corresponds to the x-chain state with an excess atom with respect to the commensurate atomic structure. The model parameters for which x-kinks in the neighbouring atomic chains attract one another and form a stable chain of x-kinks (a y-chain of x-kinks) are determined. The authors derive an effective Hamiltonian describing the behaviour of the y-chain and calculate the parameters of a y-kink (secondary kink). The applicability of the model to describe the dynamics of quasi-two-dimensional atomic layers adsorbed on metal surfaces is discussed.