High-resolution (v/Av ~ 30,000) spectra of Jupiter and Saturn were obtained in order to study the composition and dynamics of Jupiter and Saturn. The shapes of CO absorption lines in Jupiter are broad, consistent with line formation at F ~ 2-9 bars. This is strong evidence in favor of internal mixing as the source of CO in Jupiter. Further, we find that the O abundance at 1100 K must be nearly solar. No variations in CO abundance were found between the North Equatorial Belt, the North Tropical Zone, and the Great Red Spot. Because CO is very sensitive to variations in the rate of mixing, we conclude that there are no gross variations in mixing with location on Jupiter. We observed CO in Saturn for the first time. The source of CO in Saturn is uncertain, although theoretical arguments favor an external source to an internal one. If the rings of Saturn are the source of the oxygen that eventually leads to CO in Saturn, the rate of influx required imposes an upper limit to the lifetime of the rings off < 100 million years. We have also found the first evidence for GeH4 in the atmosphere of Saturn. Absorption lines in the P and R branch of GeH4 are observed although no evidence of the stronger Q branch is found. We postulate that scattered solar radiation may be responsible for altering the thermal spectrum in regions of very low flux such as the Q -branch region. The abundance of GeH4 is consistent with the expected disequilibration from internal mixing in Saturn. Finally, we found more acetylene in the stratosphere of Saturn as compared to Jupiter, indicating possibly faster mixing in the upper atmosphere ofthat planet.