I'm assuming Win98SE from your profile. My comments are mostly applicable to all Windows versions, Win95 on up.
RUNDLL.EXE and RUNDLL32.EXE are executables designed to take advantage of DLLs that have been specifically written so that certain functions within them can be called from the command line, through the use of RUNDLL.EXE for 16-bit functions and the use of RUNDLL32.EXE for 32-bit functions. (NT4 and W2K only allow use of RUNDLL32.EXE.)
So this means that something along the lines of a batch process, a script, or a registry entry is trying to cause RUNDLL.EXE or RUNDLL32.EXE to either try to access and run something on the Internet, OR it is trying to cause one of the executables to run some other process that wants access to the Internet. Neither one is particularly good if you don't know why it's happening.
This could be quite innocent, like a failed installation that left behind a RUNDLL call that's still trying to run or some application you have on the system which is set to periodically access the Internet to retrieve mail or "phone home". Or it could be something like an attempt by someone or a Trojan to cause your system to establish a connection surreptitiously.
If I were you, I'd find out what's causing it. In addition to checking things like the above-mentioned items, you might get something like the "spyware" detector called Ad-Aware from
Lavasoft.
It might be helpful to those reading this thread if you provided us with a little more information. Does this seem to happen in response to something you do as a user? Does it seem to be a response to something else that happens on the system, like receipt of an email or fax or something? Does it happen only at startup? Does it happen over and over again with a regular periodicity? (To help with the troubleshooting, if you've set ZoneAlarm to not ask you any more, you'll need to get rid of the rule so that ZA starts asking you again whenever the phenomenon happens.)
I imagine there are many other possibilities, but I'm not thinking too clearly due to high pollen count and serious quantities of anti-histamines on board!
Please give us more of the sort of information I indicated, and maybe somebody will have a bright idea.
Regards,
Jim
Ooops! Sorry, I meant to include a couple of links to some general info on the RUNDLL functions.
http://support.microsoft.com/support/kb/articles/Q164/7/87.asp
http://www.microsoft.com/TechNet/IE/reskit/ie5/part3/ch18post.asp
Nothing specific to your situation, but some info that mike make a light bulb light up.