  A cross between two well-known integrable multi-particle dynamics, an affine
Toda molecule and a Sutherland system, is introduced for any affine root
system. Though it is not completely integrable but partially integrable, or
quasi exactly solvable, it inherits many remarkable properties from the
parents. The equilibrium position is algebraic, i.e. proportional to the Weyl
vector. The frequencies of small oscillations near equilibrium are proportional
to the affine Toda masses, which are essential ingredients of the exact
factorisable S-matrices of affine Toda field theories. Some lower lying
frequencies are integer times a coupling constant for which the corresponding
exact quantum eigenvalues and eigenfunctions are obtained. An affine
Toda-Calogero system, with a corresponding rational potential, is also
discussed.
