  Bloch's conjecture for a surface $X$ over an algebraically closed field $k$
states that every homologically trivial correspondence $\Gamma $ acts as 0 on
the Albanese kernel $T(X_{\Omega})$, where $\Omega $ is a universal domain
containing $k$. Here we prove that, for a complex K3 surface $X$, Bloch's
conjecture is equivalent to the existence of a valence for every
correspondence. We also give applications of this result to the case of a
correspondence associated to an automorphisms of finite order and to the
existence of constant cycle curves on $X$. Finally we show that Franchetta's
conjecture, as stated by K.O'Grady, holds true for the family of polarized K3
surfacees of genus $g$, if $ 3 \le g \le 6$
