  We determine the physical parameters (magnetic field and Doppler factor) of
the homogeneous synchrotron self-Compton model allowed by the observed X-ray to
gamma-ray spectra and variability of Markarian~501 during the 15-16 April 1997
flaring activity. We find that magnetic fields between 0.07 G and 0.6 G and
Doppler factors between 12 and 36 could fit (depending on observed variability
time scale) these observations. We take account of photon-photon pair
production interactions of gamma-ray photons occurring both inside the emission
region and during propagation to Earth and find these to be extremely important
in correctly determining the allowed model parameters. Previous estimates of
the allowed parameter space have neglected this effect. Future multi-wavelength
campaigns during strong flaring activity, including observations from optical
to TeV gamma-rays, should enable the physical parameters to be further
constrained.
