An equatorial wave whose dispersion relation is asymptotic to that for equatorial Kelvin waves for large positive (eastward) zonal wavenumbers and asymptotic to equatorial Rossby waves for large negative (westward) zonal wavenumbers. Rossby-gravity waves are also called Yanai waves and ``mixed Rossby-gravity waves. In the shallow water approximation, the dispersion relationship is given by frequency omega= k c (1-(1+4�eta/(k^2 c))^(1/2))/2, in which k is the zonal wavenumber, �eta is the meridional gradient of the Coriolis parameter at the equator, and c=(gH)^(1/2) for which g is the acceleration of gravity and H is the mean fluid depth.