  In this paper, charged Higgs pair production through $\ell^+ \ell^-
\rightarrow H^+ H^-$ where $\ell = e$ or $\mu$, is studied within the framework
of a general Two Higgs Doublet Model (2HDM). The analysis is relevant to a
future $e^+e^-$ or $\mu^+\mu^-$ collider operating at center of mass energy of
$\sqrt{s}=500$ GeV. Two different scenarios of small and large $\alpha$ values
is studied. Here $\alpha$ is the parameter which diagonalizes the neutral
CP-even Higgs boson mass matrix. Within the Minimal Supersymmetric Standard
Model (MSSM), cross section of this process is almost the same at $e^+e^-$ and
$\mu^+\mu^-$ colliders. It is shown that at $e^+e^-$ colliders within a general
2HDM, cross section is not sensitive to the mass of neutral Higgs bosons,
however, it can acquire large values up to several picobarn at $\mu^+\mu^-$
colliders with the presence of heavy neutral Higgs bosons. A scan over Higgs
boson mass parameter space is performed to analyze the effect of large masses
of neutral Higgs bosons involved in the s-channel propagator and thus in the
total cross section of this process.
