The simulation of the Madden-Julian Oscillation (MJO) and convectively coupled equatorial waves (CCEWs) is considered in 13 state-ofthe-art models from phase 6 of the Coupled Model Intercomparison Project (CMIP6). We use frequency-wavenumber power spectra of the models and observations for Outgoing Longwave Radiation (OLR) and zonal winds at 250 hPa (U250), and consider the historical simulations and end of 21st century projections for the SSP245 and SSP585 scenarios.The models simulate a spectrum quantitatively resembling that observed, though systematic biases exist. MJO and Kelvin waves (KW) are mostly underestimated, while equatorial Rossby waves (ER) are overestimated. Most models project a future increase in power spectra for the MJO, while nearly all project a robust increase for KW and weaker power values for most other wavenumber-frequency combinations, including higher wavenumber ER. In addition to strengthening, KW also shift toward higher phase speeds (or equivalent depths). Models with a more realistic MJO in their control climate tend to simulate a stronger future intensification.