This came up at Sunday School today. The exact words used aren't in my head anymore, but the gist was

Does a Christian have

A. One nature ( the new one ) plus a tendency to and struggle against sin. The old (flesh) nature is completely dead and no longer exists in the Christian.
B. Both natures: the new and the old one. The old nature, even though dead, must still be struggled with.
C. Other

I'm sure my description above is not very precise.