Amplitudes in Nonlocal Theories at High Energies

We obtain the upper bound for the total scattering cross section $\sigma_{\text{tot}}(s)\leq Cs^{\rho-1}\ln^2s$ in the nonlocal quantum field theory of a scalar field with a bounded amplitude growth $\sim e^{B\|p^2\|^\rho}$ in the complex momentum $p^2$-space.