Simultaneous in situ measurements of N sub(2) O and CH sub(4) were made with a tunable diode laser spectrometer (ALIAS II) aboard the Observations from the Middle Stratosphere (OMS) balloon platform from New Mexico, Alaska, and Brazil during 1996 and 1997. We find different compact relationships of CH sub(4) with N sub(2) O in the tropics and extra-tropics because mixing is slow between these regions. Transport into the extra-tropics from the tropics or the polar vortex leads to deviations from the normal compact relationship. We use measured N sub(2) O and CH sub(4) and a simple model to quantify entrainment of mid-latitude stratospheric air into the tropics. The entrainment time scale is estimated to be 16 (+17,-8) months for altitudes between 20 and 28 km. The fraction of tropical air entrained from the extra-tropical stratosphere is 50% (+18%, -30%) at 20 km, increasing to 78% (+11%, -19%) at 28 km.