Dwarf (or dark) molecular clouds and molecular clumps have a lifetime
which is greater than their dynamical time and must therefore be, in a
n average sense, in mechanical equilibrium. Equilibrium perpendicular
to a global magnetic field is by magnetic forces and it is proposed th
at along the field the gas is supported by an Alfven wave pressure for
ce. A self-consistent analytical model, utilising a WKB approximation,
is developed for such support. It is found that Alfven waves are inde
ed a good candidate for this support, generating model cloud thickness
es consistent with observations. The effect of damping by the linear p
rocess of ion-neutral friction is considered. It is found that the dam
ping of the waves is not a necessary condition for the support of the
cloud although weak damping is an advantage. The possible sources of t
hese waves are discussed.