  In certain mild extensions of the Standard Model, spin-independent long range
forces can arise by exchange of two very light pseudoscalar spin--0 bosons. In
particular, we have in mind models in which these bosons do not have direct
tree level couplings to ordinary fermions. Using the dispersion theoretical
method, we find a $1/r^{3}$ behaviour of the potential for the exchange of very
light pseudoscalars and a $1/r^{7}$ dependence if the pseudoscalars are true
massless Goldstone bosons.
