We, point out that present experimental limits from searches for neutr
al Higgs bosons at LEP already imply stringent lower bounds on the mas
s of the charged Higgs boson in the Minimal Supersymmetric Standard Mo
del (MSSM); these bounds are especially severe for low values of tan b
eta (tan beta less than or equal to 3), where the H+(t) over bar b cou
pling is large. However, these indirect constraints are much weaker in
simple extensions of the MSSM Higgs sector involving the introduction
of an extra U(1) gauge group or an extra SU(2) X U(1)(y) Higgs single
t field; in the latter case charged Higgs bosons can even be light eno
ugh to be pair produced at LEP. (C) 1998 Published by Elsevier Science
B.V. All rights reserved.