The convective equatorial waves in the NCEP/NCAR reanalysis and intermediate complexity atmospheric model QTCM are studied on the base of double space-time spectral analysis. The frequency-wavenumber spectra of outgoing longwave radiation, precipitation, zonal wind stress and net heat flux are obtained. Further, the propagation characteristics, amplitude and seasonal variability of filtered waves are analyzed. It is shown that QTCM simulates a wide variety of equatorial waves that share many characteristics with the observations. It is suggested that convective scheme applied in the model allows for simulation of interaction at interannual-intraseasonal time scales. The role of interannual SST forcing and extratropical excitation is elucidated using the model's experiments with specific boundary conditions.