[en] In previous work one of the authors gave a geometric theory of those nonlinear evolution equations which can be solved by the Zakharov and Shabat (1972) inverse scattering scheme as generalized by Ablowitz, Kaup, Newell and Segur (1973,1974). In this paper the authors extend the geometric theory to include the Hamiltonian structure of those NEEs solvable by the method, and indicate the connection between the geometric theory and the theory of prolongation structures and pseudopotentials due to Wahlquist and Estabrook (1975,1976). They exploit a 'gauge' invariance of the geometric theory to derive both the well known polynomial conserved densities of the sine-Gordon equation and a non-local set of conserved densities which act as Hamiltonian densities for a hierarchy of sine-Gordon equations analogous to that found by Lax (1968) for the Korteweg-de Vries equation and which appears to be new. In an appendix an expression is derived for the equation of motion for an arbitrary member of the sine-Gordon hierarchy by methods which can be applied in larger context. (Auth.)