  After a brief review (in the first part) of some relevant properties of the
high-energy parton-parton scattering amplitudes, in the second part we shall
discuss the infrared finiteness and some analyticity properties of the
loop-loop scattering amplitudes in gauge theories, when going from Minkowskian
to Euclidean theory, and we shall see how they can be related to the still
unsolved problem of the s-dependence of the hadron-hadron total cross-sections.
