Abstract: We have observed fluctuations, manifested as sub-nanosecond to nanosecond transient, millivolt-amplitude voltage pulses, generated in two-dimensional NbN nanobridges, as well as in extended superconducting meander nanostructures, designed for single photon counting. Both nanobridges and nano-stripe meanders were biased at currents close to the critical current and measured in a range of temperatures from 1.5 to 8 K. During the tests, the devices were blocked from all incoming radiation by a metallic enclosure and shielded from any external magnetic fields. We attribute the observed spontaneous voltage pulses to the Kosterlitz-Thouless-type fluctuations, where the high enough applied bias current reduces the binding energy of vortex-antivortex pairs and, subsequently, thermal fluctuations break them apart causing the order parameter to momentarily reduce to zero, which in turn causes a transient voltage pulse. The duration of the voltage pulses depended on the device geometry (with the high-kinetic inductance meander structures having longer, nanosecond, pulses) while their rate was directly related to the biasing current as well as temperature.