||We have observed, nanosecond-in-duration, transient voltage pulses, generated across two-dimensional (2-D) NbN stripes (width: 100--500 nm; thickness: 3.5--10 nm) of various lengths (1--500 μm), when the wires were completely isolated from the outside world, biased at currents close to the critical current, and kept at temperatures below the mean-field critical temperature Tco. In 2-D superconducting films, at temperatures below the Kosterlitz-Thouless transition, all vortices are bound and the resistance is zero. However, these vortices can get unbound when a large enough transport current is applied. The latter results in a transient resistive state, which manifests itself as spontaneous, 2.5--8-ns-long voltage pulses with the amplitude corresponding to the unbinding potential of a vortex pair. In our 100-nm-wide stripes, we have also observed the formation of phase slip centers (PSCs) at temperatures close to Tco, and a mixture of PSCs and unbound vortex-antivortex pairs at low temperatures.