Undelivered email to wrong address

A friend of mine keeps getting notices of undelivered emails saying he has sent emails to people with the wrong email addresses. Certainly he is not doing it. He doens’t recognize any of those email addresses.

Somebody somehow has got his email address and is using it to spam other people? What could be the source of the problem? Could it indicate there is spyware in his computer system? How can we prevent this from happening and how can we stop it now?