For a subring R of the rational numbers, we study R-localization functors in the local homotopy theory of simplicial presheaves on a small site and then in A 1 -homotopy theory. To this end, we introduce and analyze two notions of nilpotence for spaces in A 1 -homotopy theory paying attention to future applications for vector bundles. We show that R-localization behaves in a controlled fashion for the nilpotent spaces we consider. We show that the classifying space BGL n is A 1 -nilpotent when n is odd, and analyze the (more complicated) situation where n is even as well. We establish analogs of various classical results about rationalization in the context of A 1 -homotopy theory: if −1 is a sum of squares in the base field, A n \ 0 is rationally equivalent to a suitable motivic Eilenberg-Mac Lane space, and the special linear group decomposes as a product of motivic spheres.