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In paper I of this series on fluid turbulence we showed that exactresummations of the perturbative theory of the structure functions of velocitydifferences result in a finite (order by order) theory. These findings excludeany known perturbative mechanism for anomalous scaling of the velocitystructure functions. In this paper we continue to build the theory ofturbulence and commence the analysis of nonperturbative effects that form theanalytic basis of anomalous scaling. Starting from the Navier-Stokes equations(at high Reynolds number Re) we discuss the simplest examples of the appearanceof anomalous exponents in fluid mechanics. These examples are the nonlinear(four-point) Green's function and related quantities. We show that therenormalized perturbation theory for these functions contains ``ladder``diagrams with (convergent!) logarithmic terms that sum up to anomalousexponents. Using a new sum rule which is derived here we calculate the leadinganomalous exponent and show that it is critical in a sense made precise below.This result opens up the possibility of multiscaling of the structure functionswith the outer scale of turbulence as the renormalization length. Thispossibility will be discussed in detail in the concluding paper III of thisseries.Comment: PRE in press, 15 pages + 21 figures, REVTeX, The Eps files of figures  will be FTPed by request to fnlvov@wis.weizmann.ac.i

Exact resummations in the theory of hydrodynamic turbulence. II. A ladder to anomalous scaling