The properties of theoretical modes of the Madden-Julian intraseasonal oscillation (MJO) and convectively coupled equatorial waves are compared with observational studies. The theoretical modes have been obtained using a global two-level primitive equation instability model incorporating parameterizations for evaporation-wind feedback, cumulus convection and dissipation. The evaporation has been specified through a bulk aerodynamic formula and the convection through a generalized Kuo-type parameterization. The genesis mechanisms for the formation of intraseasonal oscillations and equatorially trapped waves including Kelvin waves, equatorial Rossby waves, mixed Rossby-gravity waves, and eastward inertio-gravity waves are analyzed. Both three-dimensional and zonally averaged basic states for January 1979 have been employed and the e-folding times, periods, structures and propagation characteristics of these waves have been analyzed and compared with their observed properties. The intraseasonal oscillations are particularly realistic when the three-dimensional basic state includes evaporation-wind feedback, which promotes the zonal wavenumber 1 component of the eastward propagating velocity potential, and cumulus convection. The tropical-extratropical interactions of the model MJO are analyzed. The links and phase relationships between tropical convection in the theoretical MJO and the Antarctic Oscillation and North Atlantic Oscillation agree closely with the studies of L'Heureux and Higgins (2008) and Lin et al. (2009). Wave fluxes associated with the model MJO are also very similar to those based on observations. With evaporation-wind feedback, the model equatorially trapped Kelvin, equatorial Rossby, mixed Rossby-gravity and eastward inertio-gravity waves have periods, structures and propagation characteristics closely comparable with the corresponding observed waves of Wheeler and Kiladis (1999).