Single-strand-preferring ribonucleases of the pancreatic type, structurally and/or catalytically similar to bovine RNase A but endowed with a higher protein basicity, are able to degrade double-stranded RNA (dsRNA) or DNA:RNA hybrids under standard assay conditions (0.15 M NaCl, 0.015 M sodium citrate, pH 7), where RNase A is inactive. This enzyme too, however, becomes quite active if assay conditions are slightly modified or its basicity is increased (polyspermine-RNase). In the attempt to review these facts, we have analyzed and discussed the role that in the process have the secondary structure of dsRNA as well as other variables whose influence has come to light in addition to that of the basicity of the enzyme protein, i.e., the ionic strength, the presence of carbohydrates on the RNase molecule, and the structure (monomeric or dimeric) of the enzyme. A possible mechanism by which dsRNAs are attacked by pancreatic-type RNases has been proposed.