  We consider the double-elliptic generalisation of dynamical systems of
Calogero-Toda-Ruijsenaars type using finite-dimensional Mukai-Sklyanin
algebras. The two-body system, which involves an elliptic dependence both on
coordinates and momenta, is investigated in detail and the relation with Nambu
dynamics is mentioned. We identify the 2D complex manifold associated with the
double elliptic system as an elliptically fibered rational ("1/2K3 ") surface.
Some generalisations are suggested which provide the ground for a description
of the N-body systems. Possible applications to SUSY gauge theories with
adjoint matter in $d=6$ with two compact dimensions are discussed.
