  Asymptotic behavior of the scattering amplitude for two scalar particles by
scalar, vector and tensor exchanges at high energy and fixed momentum transfers
is reconsidered in quantum field theory. In the framework of the
quasi-potential approach and the modified perturbation theory a systematic
scheme of finding the leading eikonal scattering amplitudes and its corrections
are developed and constructed. The connection between the solutions obtained by
quasi-potential and functional approaches is also discussed. The first
correction to leading eikonal amplitude is found.
