  We present a time-dependent spectral model of the nebula 3C58 and compare it
with available data. The model is for a leptonic nebula, in which particles are
subject to synchrotron, inverse Compton, self-synchrotron Compton, adiabatic,
and bremsstrahlung processes. We find that 3C58 is compatible with being a
particle dominated nebula, with a magnetic field of 35$\mu$G. A broken power
law injection fits well the multi-frequency data, with a break energy at about
40 GeV. We find that 3C58 is not expected to appear in VERITAS or MAGIC II,
unless the local IR background is a factor of \sim20 off Galactic models
averages. For cases in which the CMB dominates the inverse Compton
contribution, we find that 3C58 will not be visible either for the Cherenkov
Telescope Array.
