Recent studies report that two types of El Nio events have been observed. One is the cold tongue El Nio or Eastern Pacific El Nio (EP El Nio), which is characterized by relatively large sea surface temperature (SST) anomalies in the eastern Pacific, and the other is the warm pool El Nio (a.k.a. 'Central Pacific El Nio' (CP El Nio) or 'El Nio Modoki'), in which SST anomalies are confined to the central Pacific. Here the vertical structure variability of the periods during EP and CP is investigated based on the GFDL_CM2.1 model in order to explain the difference in equatorial wave dynamics and associated negative feedback mechanisms. It is shown that the mean stratification in the vicinity of the thermocline of the central Pacific is reduced during CP El Nio, which favours the contribution of the gravest baroclinic mode relatively to the higher-order slower baroclinic mode. Energetic Kelvin and first-meridional Rossby wave are evidenced during the CP El Nio with distinctive amplitude and propagating characteristics according to their vertical structure (mostly first and second baroclinic modes). In particular, the first baroclinic mode during CP El Nio is associated to the ocean basin mode and participates to the recharge process during the whole El Nio cycle, whereas the second baroclinic mode is mostly driving the discharge process through the delayed oscillator mechanism. This may explain that the phase transition from warm to neutral/cold conditions during the CP El Nio is delayed and/or disrupted compared to the EP El Nio. Our results have implications for the interpretation of the variability during periods of high CP El Nio occurrence like the last decade.