Inclusive processes at high energies

New physical characteristics for inclusive processes are discussed: these are the mean particle multiplicities in different regions of phase space. The hypotheses of pionization, scale invariance, and limiting fragmentation are discussed from the point of view of analyticity and unitarity. The upper bound for the cross section $d^2\sigma_{ab\to cd}/d\cos\theta d\varphi$ is improved. It is shown that with the chosen assumptions concerning the analytieity the estimate that is obtained cannot be improved in the sense of a power dependence on the energy.