  We introduce braided Dunkl operators that are acting on a q-polynomial
algebra and q-commute. Generalizing the approach of Etingof and Ginzburg, we
explain the q-commutation phenomenon by constructing braided Cherednik algebras
for which the above operators form a representation. We classify all braided
Cherednik algebras using the theory of braided doubles developed in our
previous paper. Besides ordinary rational Cherednik algebras, our
classification gives new algebras attached to an infinite family of subgroups
of even elements in complex reflection groups, so that the corresponding
braided Dunkl operators pairwise anti-commute. We explicitly compute these new
operators in terms of braided partial derivatives and divided differences.
