  We consider generalizations of Dunkl's differential-difference operators
associated with groups generated by reflections. The commutativity condition is
equivalent to certain functional equations. These equations are solved in many
cases. In particular, solutions associated with elliptic curves are
constructed. In the $A_{n-1}$ case, we discuss the relation with elliptic
Calogero-Moser integrable $n$-body problems, and discuss the quantization
($q$-analogue) of our construction.
