Logarithmically rising hh and γ 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 require a Pomeron intercept above one. The very important r\^ole of the preasymptotic contributions is especially emphasized.