Static variables exist for the lifetime of the application domain that contains them. In the case of a web service, this is usually an ASP.Net Worker process. This means that when IIS decides to run a workflow loop, your static variable will disappear. This may be what you want, in which case it is probably a good choice. (I believe that they are discussing whether or not the static variables are correct in this context).
As part of the web service, you also have access to the HttpApplicationState through the Application property (this will be the asmx service ... not sure if the WCF is the same or not), so this could also be a good choice for storing something that is necessary for the lifetime service.
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