- We suggest a new procedure for extrapolating the parton distributions from HERA to much higher energies. The procedure suggested consists of two steps. First, we solve the non-linear evolution equation. Second, we introduce a correcting function for which we write a DGLAP-type linear evolution equation. The nonlinear equation is solved numerically and estimates for the saturation scale, as well as for the gluon density at THERA and LHC energies are made.