Evolution of a polyion and an electrically uncharged macromolecule in confined environment, represented by a tight nanopore, induced by external electric field, is investigated. The motion of the uncharged macromolecule is forced by the polyion. In suitably selected conditions, the collision between macromolecules, compression of the uncharged macromolecule, and finally the swap of positions of macromolecules in the nanochannel are observed by means of the nonequilibrium Monte Carlo method on the lattice. The exemplary trajectories of macromolecules, their geometry, and energetics are analyzed. The dependence of the time of swapping on the number of macromolecule beads is described by scaling laws.