Planetary-scale equatorial waves play an important role in the dynamics of the tropical atmosphere. They are believed to be excited in unsteady convective heating in the tropical troposphere. From convective centers in the intertropical convergence zone (ITCZ), equatorial waves propagate vertically into the upper atmosphere where they are eventually absorbed, e.g., through radiative dissipation. A spectrum of vertically propagating Kelvin waves was revealed to be trapped about the equator, radiating vertically out of the tropical troposphere. Two other Kelvin waves were found with phase velocities 2 and 4 times as fast. The ultrafast Kelvin wave move at nearly 120 m/s and are seen to propagate to the highest altitude observed by Nimbus-7 LIMS. Each class has the form of a Kelvin wave, a Gaussian centered on the equator and propagating vertically, and all satisfy the dispersion relationship for equatorial Kelvin waves. These vertically propagating Kelvin waves account for a substantial fraction of the temperature variability in the tropical stratosphere. In combination, they lead to temperature fluctuations in excess of 5K in the upper stratosphere and mesosphere. Because several chemical constituents are photochemically controlled in this region, vertically propagating Kelvin waves are expected to lead to variations in the abundances of such species. Through temperature sensitivity of their chemical rate coefficients, several species should respond photochemically to the fluctuating wave field.