Normal endomorphisms of von Neumann algebras need not be extendable 
to automorphisms of a larger von Neumann algebra, but they always 
have asymptotic lifts.  We describe the structure of endomorphisms 
and their asymptotic lifts in some detail, and apply those results 
to complete the identification of asymptotic lifts of unital completely 
positive linear maps on von Neumann algebras in terms of their minimal dilations 
to endomorphisms.