The mitochondrial DEAD-box proteins Mss116p of Saccharomyces cerevisiae and CYT-19 of Neurospora crassa are ATP-dependent helicases that function as general RNA chaperones. The helicase core of each protein precedes a C-terminal extension and a basic tail, whose structural role is unclear. Here we used small-angle X-ray scattering to obtain solution structures of the full-length proteins and a series of deletion mutants. We find that the two core domains have a preferred relative orientation in the open state without substrates, and we visualize the transition to a compact closed state upon binding RNA and adenosine nucleotide. An analysis of complexes with large chimeric oligonucleotides shows that the basic tails of both proteins are attached flexibly, enabling them to bind rigid duplex DNA segments extending from the core in different directions. Our results indicate that the basic tails of DEAD-box proteins contribute to RNA-chaperone activity by binding nonspecifically to large RNA substrates and flexibly tethering the core for the unwinding of neighboring duplexes.