  Most of current models of TeV blazars emission assume a Synchrotron
Self-Compton mechanism where relativistic particles emit both synchrotron
radiation and Inverse Compton photons. For sake of simplicity, these models
usually consider only steady state emission. The spectral features are thus
only related to the shape of the particle distribution, and do not depend on
the timing of observations. In this letter, we study the effect of, firstly,
the lag between the beginning of the injection of the fresh particles and the
trigger of the observation, and secondly, of a finite injection duration. We
illustrate these effects considering an analytical time-dependent model of the
synchrotron emission by a monoenergetic distribution of leptons. We point out
that the spectral shape can be in fact very dependent on observational
conditions if the particle injection term is time-dependent, particularly
taking into account the effect of the time averaging procedure on the final
shape of the SED. Consequences on the acceleration process are also discussed.

Astrophysics