  Pre-main sequence stars are variable sources. In stars with disks, this
variability is related to the morphology of the inner circumstellar region
(<0.1 AU) and that of the photosphere and corona, all impossible to be
spatially resolved with present day techniques. This has been the main
motivation for the Coordinated Synoptic Investigation of NGC 2264. In this
paper, we focus on the stars with disks. We analyze the X-ray spectral
properties extracted during optical bursts and dips in order to unveil the
nature of these phenomena. We analyze simultaneous CoRoT and Chandra/ACIS-I
observations to search for coherent optical and X-ray flux variability in stars
with disks. Then, stars are analyzed in two different samples. In stars with
variable extinction, we look for a simultaneous increase of optical extinction
and X-ray absorption during the optical dips; in stars with accretion bursts,
we search for soft X-ray emission and increasing X-ray absorption during the
bursts. Results. We find evidence for coherent optical and X-ray flux
variability among the stars with variable extinction. In 9/24 stars with
optical dips, we observe a simultaneous increase of X-ray absorption and
optical extinction. In seven dips, it is possible to calculate the NH/AV ratio
in order to infer the composition of the obscuring material. In 5/20 stars with
optical accretion bursts, we observe increasing soft X-ray emission during the
bursts that we associate to the emission of accreting gas. It is not surprising
that these properties are not observed in all the stars with dips and bursts,
since favorable geometric configurations are required. The observed variable
absorption during the dips is mainly due to dust-free material in accretion
streams. In stars with accretion bursts, we observe on average a larger soft
X-ray spectral component not observed in non accreting stars.
