I have six computers on my home network consisting of 1 WinME, 1 XP Media Center, 1 XP Pro and 3 XP Home. They all belong to one workgroup. In "My Network Places", on all machines, there is now another network named "Workgroup". I have no idea where it came from. I am also having connection issues on the LAN. Sometimes the data transfer between some of the machines comes to a complete stop. Does anyone have an idea on how to resolve this problem?

more info would help
router - manufacturer
switch - manufacturer
Your ip address assigned dynamic or did you setup static
the data transfer issues some of the machines - which ones is the WinMe always involved? i'll check back for your reply

You did not say if your network is part WiFi; this other group may come via WiFi if you have poor or no security.

What type of Speed Wireless Router are you using? G, G+, N ?

did you have all the computers joined the work group, if you don't run the configuration to have each one join the work group you will have more that one Work group showing up, because this is the default for windows i suggest you give the work group a unique name, like (your name or initial work group)