Recent evidence has suggested the existence of sense-antisense transcription in mammals, but the existence of double-stranded RNAs endowed with biological function has remained elusive. Herein we show that hundreds of putative natural double-stranded RNAs (ndsRNAs) are expressed from interspersed genomic locations and respond to cellular cues. We demonstrate that a subset of ndsRNAs localize in the nucleus and, in their double-stranded form, interact with nuclear proteins. Detailed characterization of an ndsRNA (nds-2a) revealed that this molecule displays differential localization throughout the cell cycle and directly interacts with RCC1 and RAN and, through the latter, with the mitotic RANGAP1-SUMO1-RANBP2 complex. Notably, altering nds-2a levels led to postmitotic abnormalities, mitotic catastrophe and cell death, thus supporting a mitosis-related role. Altogether, our study reveals a hitherto-unrecognized class of RNAs that potentially participate in major biological processes in human cells.