  Blazars are highly variable sources over timescales that can be as low as
minutes. This is the case of the High Energy Peaked BL Lac (HBL) objects
showing strong variability in X-rays, which highly correlate with that of the
TeV emission. The degree of this correlation is still debated, particularly
when the flaring activity is followed down to very short time scales. This
correlation could challenge the synchrotron-self-Compton scenario in which one
relativistic electron population dominates the entire radiative output. We
argue that the LOFT Large Area Detector (10 m$^2$, LAD), thanks to its
unprecedented timing capability, will allow us to detect the X-ray counterpart
(2-50 keV) of the very fast variability observed at TeV energies, sheding light
on the nature of X-TeV connection. We will discuss the test case of PKS
2155-304, showing as it would be possible to look for any X-ray variability
occurring at very short timescales, never explored so far. This will put strong
constraints on the size and the location of any additional electron population
in the multi-zone scenario. Under this perspective, LOFT and the CTA
observatories, planned to operate in the same time frame, will allow us to
investigate in depth the connection between X-ray and TeV emissions. We also
discuss the potentialities of LOFT in measuring the change in spectral
curvature of the synchrotron spectra in HBLs which will make possible to
directly study the mechanism of acceleration of highly energetic electrons.
LOFT timing capability will be also promising in the study of Flat Spectrum
Radio Quasars (FSRQs) with flux $\ge 1$ mCrab. Constraints to the location of
the high energy emission will be given by temporal investigation on second
timescale and spectral trend analysis on minute timescales. This represents a
further link with CTA because of the rapid (unexpected) TeV emission recently
detected in some FSRQs.
