  The charged Higgs associated production with a W boson has a smooth cross
section as a function of the charged Higgs mass at muon colliders. The cross
section in Minimal Supersymmetric Standard Model is about 25fb in the range 200
GeV < mH < 400 GeV with tanbeta = 50. This is much larger than the
corresponding cross section at an e+e- collider which reaches a fraction of
femtobarn. The observability of this channel at a muon collider has been
recently studied in an earlier work leading to the result that with 1 ab-1, a
5sigma signal can be observed throughout the aforementioned mass range. In this
paper, results of a study based on a general two Higgs doublet model (type II
and III) are presented and the cross section of this process in the most
sensitive parameter space is evaluated. It is concluded that the cross section
of this process increases with increasing neutral Higgs boson masses involved
in the s-channel diagram and can be as large as several picobarn with tanbeta =
50. The region of "physical Higgs boson mass" parameter space which could lead
to a 5 sigma signal at 50fb-1 is specified.
