Have you checked to see if your firewall is blocking anything related to Avast?
Did you just upgrade or install Avast? I need more information from you re: your situation: OS, what product and version of Avast you are using, how you connect to the Internet, did you check your modem (if you use one), etc.
When was the last time you updated your virus definitions?
Did you try rebooting your machine, then try updating at a later time? Often this does the trick.
