The general rule is, only one Firewall and only one anti-virus.
Specifically, that means have only one anti-virus which is set to scan in the background continuously. While it is OK to have more then one AV scanner, make sure that the others do not run in the background otherwise there can be conflicts as they attempt to scan the same data at the same time.
I don't know WLE, (Windows Live Essentials), at all, but if it has options to disable background scanning then I see no reason why you can't keep it installed and use it for the occasional manual scan.
Since most AVs now include anti-spyware scanning as well, make sure that any anti-spyware components that WLE has are also disabled.
Does that help?
Mark
I downloaded Avast Antivirus 6 (free) and I'm very happy with it; however, I see that Windows Essential Security is also running.
Is it possible to keep both of these programs running or should I de-activate Windows Essential Security? And how do I do that without losing the other Windows Essential programs?

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