Endomorphisms of continuous Cuntz algebras

We establish a one to one correspondence between endomorphisms of Arveson's continuous analogues C*(E) of the Cuntz algebras and certain cocycles. For the analogues of quasi-free automorphism groups there are no positive gauge invariant EMS-weights, whereas for the gauge action there exists a non lower semi-continuous ground weight on C-(E). Crossed products by quasi-free actions are often simple.