- We suggest a new procedure for extrapolating the parton distributions from HERA energies to higher energies at (THERA, LHC). The procedure suggested consists of two steps: first, we solve the nonlinear evolution equation which includes the higher-twist contributions, however this equation is deficient due to the low (log(1/ x )) accuracy of our calculations. Second, we introduce a correcting function for which we write a DGLAP type linear evolution equation. We show that this correcting function is small in the whole kinematic region and decreases at low x . The nonlinear evolution equation is solved numerically and first estimates for the saturation scale, as well as for the value of the gluon density at THERA and LHC energies are made. We show that nonlinear effects lead to damping of the gluon density by a factor of 2–3 at x ≈10 −7 .