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We discuss how the dijet azimuthal correlations in DIS and real photoproduction at HERA probe the differential (unintegrated) gluon distribution in the proton. We find a strong dependence of the azimuthal correlation pattern on Bjorken-x, photon virtuality and the cut on the jet transverse momenta. A rise of the azimuthal decorrelations is observed with decreasing Bjorken-x due to the interplay of perturbative and nonperturbative effects. We predict a strong rise of the same-side jet rate with photon energy for real photoproduction. We discuss conditions for the correlation function to be dominated by hard perturbative gluons and ways of constraining the size of the nonperturbative soft component. We make some predictions for the THERA energy range. The analysis of the energy dependence of the isolated jet and two-jet cross sections in photoproduction would be a new way to study the not yet well constrained unintegrated gluon distributions and to explore the onset of the pQCD regime. (C) 2001 Published by Elsevier Science B.V.