The Planetary Radio Astronomy instruments on Voyager 1 and 2 provided new, highly detailed measurements of several different kinds of strong, nonthermal radiation generated in the inner magnetospheres and upper ionospheres of Jupiter and Saturn. At Jupiter, an intense decameter-wavelength component (between a few tenths of a MHz and 39.5 MHz) is characterized by complex, highly organized structure in the frequency-time domain and by a strong dependence on the longitude of the observer and, in some cases, of Io. At frequencies below about 1 MHz there exists a (principally) kilometer-wavelength component of emission that is bursty, relatively broadbanded (typically covering 10 to 1000 kHz), and strongly modulated by planetary rotation. The properties of this component are consistent with a source confined to high latitudes on the dayside hemisphere of Jupiter. A second kilometric component is narrow-banded, relatively weak and exhibits a spectral peak near 100 kHz. The narrowband component also occurs periodically but at a repetition rate that is a few percent slower than that corresponding to the planetary rotation rate. This component is thought to originate at a frequency near the electron plasma frequency in the outer part of the Io plasma torus (8 to 10 R J) and to reflect the small departures from perfect corotation experienced by plasma there. The Voyager instruments also detected intense, low frequency, radio emissions from the Saturn system. The Saturnian kilometric radiation is observed in a relatively narrow frequency band between 3 kHz and 1.2 MHz, is elliptically or circularly polarized, and is strongly modulated in intensity at Saturn's 10.66-hr rotation period. This emission is believed to be emitted in the right-hand extraordinary mode from regions near or in Saturn's dayside, polar, magnetospheric cusps. Variations in intensity at Saturn's rotation period may correspond to the rotation of a localized magnetic anomaly into the vicinity of the ionospheric footprint of the polar cusp. Variations in activity on time scales of a few days and longer seem to indicate that both the solar wind and the satellite Dione can also influence the generation of the radio emission.