  We study the cross sections for the production of intermediate mass Higgs
bosons via the reactions $e^-\gamma\rightarrow \nu_eW^-\Phi^0$,
$e^-\gamma\rightarrow \nu_eH^-\Phi^0$, $e^-\gamma\rightarrow e^-Z^0\Phi^0$ and
$e^-\gamma\rightarrow e^-H^+H^-$ in the Minimal Supersymmetric Standard Model
(with $\Phi^0=H^0,h^0$ and, where possible, $A^0$) at TeV energies, taking into
account $b$--tagging capabilities. We find that the rates for
$e^-\gamma\rightarrow \nu_eW^-\Phi^0$ are large enough to permit the discovery
of at least one between $h^0$ and $H^0$ over the whole intermediate mass range
of $M_{A^0}$, at all $\tan\beta$, using the $(jj)(b\bar b)$ final state. The
${\cal {CP}}$-odd neutral $A^0$ and the charged $H^\pm$'s can be detected via
the processes $e^-\gamma\rightarrow \nu_eH^-A^0$, with $A^0\rightarrow b\bar
b$, and $e^-\gamma\rightarrow e^-H^+H^-$, resorting to the leptonic decay
$H^\pm\rightarrow \nu_\tau\tau^+(\bar\nu_\tau\tau^-)$, but only for
$M_{A^0}\approx60$ GeV. Finally, we present explicit formulae for the helicity
amplitudes of these processes.
