  We assess the potential of future electron-positron linear colliders
operating in the $e^\pm\gamma$ mode in detecting charged Higgs bosons with mass
around and larger than the top quark mass, using Compton back-scattered photons
from laser light. We compare the pair production mode, $e^-\gamma\to e^-
H^+H^-$, to a variety of channels involving only one charged Higgs scalar in
the final state, such as the tree-level processes $e^-\gamma\to \nu_e H^-
\Phi^0 $ ($\Phi^0=h^0,H^0$ and $A^0$) and $e^-\gamma\to \nu_e f\bar f H^-$
($f=b,\tau$ and $\nu_\tau$) as well as the loop-induced channel $e^-\gamma\to
\nu_e H^-$. We show that, when the charged Higgs boson mass is smaller than or
comparable to half the collider energy, $\sqrt s_{ee}\gsim 2M_{H^\pm}$, single
production cross sections are of the same size as the pair production rate,
whereas, for charged Higgs boson masses larger than $\sqrt s_{ee}/2$, all
processes are heavily suppressed. In general, production cross sections of
charged Higgs bosons via $e^\pm\gamma$ scatterings are smaller than those
induced at an $e^+e^-$ collider and the latter represents a better option to
produce and analyse such particles.
