Context : The young cluster NGC 2264 was observed with the Corot satellite for 23 days uninterruptedly in March 2008 with unprecedent photometric accuracy .
We present here the first results of the analysis of the accreting population that belongs to the cluster and was observed by Corot .

Aims : We intended to look for possible light curve variability of the same nature as that observed in the classical T Tauri star AA Tau , which was attributed to a magnetically controlled inner disk warp .
The inner warp dynamics is directly associated with the interaction between the stellar magnetic field and the inner disk region .

Methods : We analysed the Corot light curves of 83 previously known classical T Tauri stars that belong to NGC 2264 and classified them according to their morphology .
We also studied the Corot light curve morphology as a function of a Spitzer -based classification of the star-disk systems .

Results : The classification derived on the basis of the Corot light curve morphology agrees very well with the Spitzer IRAC-based classification of the systems .
The percentage of AA Tau-like light curves decreases as the inner disk dissipates , from 40 % \pm 10 % in systems with thick inner disks to 36 % \pm 16 % in systems with anemic disks and none in naked photosphere systems .
Indeed , 91 % \pm 29 % of the CTTS with naked photospheres exhibit pure spot-like variability , while only 18 % \pm 7 % of the thick disk systems do so , presumably those seen at low inclination and thus free of variable obscuration .

Conclusions : AA Tau-like light curves are found to be fairly common , with a frequency of at least \sim 30 to 40 % in young stars with inner dusty disks .
The temporal evolution of the light curves indicates that the structure of the inner disk warp , located close to the corotation radius and responsible for the obscuration episodes , varies over a timescale of a few ( \sim 1-3 ) rotational periods .
This probably reflects the highly dynamical nature of the star-disk magnetospheric interaction .