The relationship between stratospheric CH4 and Hydrogen Fluoride (HF) observed simultaneously by the Halogen Occultation Experiment (HALOE) on the Upper Atmosphere Research Satellite (UARS) has been examined globally. The meridional structures of the two long-lived species for the equinox and solstice seasons are found to be very similar. Their surfaces of constant mixing ratio, however, are found to not quite coincide. The isopleth of CH4 graphed as pressure versus latitude shows a steeper slope than that of HF. This feature can be clearly seen from the scatterplots of CH4 versus HF for a sequence of latitude regions. In general, CH4--HF correlation plots are characterized by tightly fitted curves for different latitude bands; curves for the tropics and high latitudes define the envelope for the correlations. The NCAR two-dimensional model simulation of CH4 and HF agrees well with HALOE observations, and it shows that the altitude-latitude dependences of CH4 removal and HF production rates play an important role in determining global CH4--HF correlations. It is found that the CH4--HF correlation inside the Antarctic vortex is nearly linear and is shifted from that of outside the vortex and from that of polar late-summer before the formation of the vortex. HALOE observations of CH4 and HF indicate that the two species are not in states of perfect ''slope equilibrium'' or ''gradient equilibrium'' globally. The obvious shift of HF values on CH4 surfaces or vice versa is usually found across dynamical barriers. There is no universal relationship between CH4 and HF. The HF mixing ratios are observed to change up to 20--35% for a given CH4 from different dynamically isolated regions such as the polar vortex, midlatitudes, and the tropics, and the same magnitudes of change in CH4 could also be found for a fixed HF. Therefore one must be cautious in the usage of correlation-inferring methods for any pair of tracers in place of unavailable measurements or for evaluating chemical disturbances. ¿ American Geophysical Union 1995