By analogy with Poincare waves in a channel, these are inertio-gravity waves confined to a region about the equator. The meridional velocity of the n'th mode of these waves has meridional structure of the form exp(-y^2/2R^2) H_n(y/R), in which y is the meridional distance from the equator, R is the equatorial Rossby deformation radius, and H_n is the n'th Hermite polynomial. In the shallow water approximation R^2=(gH)^(1/2)/eta in which, eta is the meridional gradient of the Coriolis parameter at the equator, g is the acceleration of gravity, and H is the mean fluid depth. The dispersion relation for the n'th mode (n>0) with zonal wavenumber k is given by those roots of the equation, cubic in frequency omega, ((gH)^(1/2)/eta) (-keta/omega - k^2 + omega^2/(gH)) =2n+1 for which the frequency exceeds Reta.