  The production of the \mssm\ Higgs bosons $H^0,h^0,A^0$ and $H^\pm$, in the
intermediate mass range of the $A^0$, at two different values of $\tan\beta$,
is studied at the possible CERN LEP$\otimes$LHC $ep$ collider, through $\gamma
p$ interactions, by photons generated via Compton back--scattering of laser
light. Signatures in which $H^0,h^0,A^0\ar b\bar b$ and $H^\pm\ar \tau\nu_\tau$
are considered. Flavour identification on $b$--jets is assumed. Backgrounds to
Higgs signals are computed. Explicit formulae for the helicity amplitudes of
the Higgs processes are given.
