Isotopic ($\delta^{17}$O and $\delta^{18}$O) measurements of stratospheric and mesospheric carbon dioxide (CO$_2$) and oxygen (O$_2$), along with trace species concentrations (N$_2$O, CO, and CO$_2$), were made in samples collected from a rocket-borne cryogenic whole air sampler. A large mass-independent isotopic anomaly was observed in CO$_2$, which may in part derive from photochemical coupling to ozone (O$_3$). The data also require an additional isotopic fractionation process, which is presently unidentified. Mesospheric O$_2$ isotope ratios differed from those in the troposphere and stratosphere. The cause of this isotopic variation in O$_2$ is presently unknown. The inability to account for these observations represents a fundamental gap in the understanding of the O$_2$ chemistry in the stratosphere and mesosphere.