Logarithmically rising hh and gamma h cross-sections: some features of model versus experimental data.

A Regge model of the Pomeron with intercept equal to one, leading to rising cross-sections is considered. Analysis of the experimental data on hadron and photon induced interactions is performed within the model. It is shown that the available pure hadronic data as well as data on DIS are compatible with a high energy logarithmic behaviour of cross-sections and do not requ ire a Pomeron intercept above one. The very important role of the preasympt otic contributions is especially emphasized.