The elastic scattering amplitude for neutral pseudoscalar particles is calculated in the limit of high energies and small momentum transfer. We have kept all inelastic channels in the intermediate state and exchanging only two particles. This resulting expression gives the upper and lower bounds on the total cross section $\frac{b}{s}l\ensuremath{\sigma}(s)l\frac{a}{{s}^{\ensuremath{\epsilon}}}$, where $\ensuremath{\epsilon}g0$ and $a$, $b$ are real constants. A special case of this elastic scattering amplitude is shown to be of the form suggested on the basis of the Regge theory of complex angular momentum. If the slope of the Regge trajectory is taken to be $\frac{a\ensuremath{\simeq}}{50}$ we obtain a total cross section which decreases very slowly $\ensuremath{\sigma}(s)=(\frac{k}{16\ensuremath{\pi}}){s}^{\ensuremath{-}0.005}$, where $k$ is some real constant.