It is not possible to view a computer operating in the real world, including the possibility of Trojan horse programs and computer viruses, as simply a finite realisation of a Turing machine. We consider the actions of Trojan horses and viruses in real computer systems and suggest a minimal framework for an adequate formal understanding of the phenomena. Some conventional approaches, including biological metaphors, are shown to be inadequate; some suggestions are made towards constructing virally-resistant systems.