The role of infrared and ultraviolet renormalons are discussed in context of the leading log (1/x) approximation of perturbative QCD. We generalize the BFKL equation for the case of running QCD coupling constant and show that the uncertainties related to the contribution of infrared renormalons turn out to be smaller, than the shadowing correction to the total cross section, in the region of small x. The contributions of infrared and ultraviolet renormalons to the BFKL equation are studied. It is shown that infrared renormalons generate the nonperturbative contribution of the order of √A2/Q2, which does not appear in the Wilson Operator Product Expansion. The solution of the BFKL equation with a running coupling constant is discussed.