  We study charged Higgs boson production at future electron-proton colliders
in the framework of the Minimal Supersymmetric Standard Model. We focus our
attention to the case of single-top production and decay through the channel
$t\to bH^\pm$ and of vector-scalar fusion via $W^{\pm*} \Phi^*\to H^\pm$ (where
$\Phi=H,h$ and $A$). We consider the signature $H^\pm\to \tau\nu_\tau$ and
compare it to the irreducible background from Standard Model interactions. For
$M_{H^\pm}<m_t$, the $H^\pm$ signal is accessible through lepton universality
breaking if $M_A<100-120$ GeV at both low and large values of $\tan\beta$.
Furthermore, although the bulk of the production cross section comes from
single-top events, a sizable contribution due to vector-scalar-scalar
interactions should be observable at large $\tan\beta$, this possibly offering
some insights into the structure of the scalar sector of the theory. The
possibility of the CERN collider running in the LEPXLHC mode is considered in
detail
