Is there HTTP connection limit of 2 simultaneous connections in webservices?
For example what hapens if you use webservices form ASP.NET web application?
Presumably ASP.NET is webservices client to some remote server. Does that
mean that the requests would be compete over those 2 connections? Is there a
workaround for this?

RFC 2068
8.1.4 Practical Considerations

Clients that use persistent connections SHOULD limit the number of
  simultaneous connections that they maintain to a given server. A
  single-user client SHOULD maintain AT MOST 2 connections with any
  server or proxy. A proxy SHOULD use up to 2*N connections to another
  server or proxy, where N is the number of simultaneously active
  users. These guidelines are intended to improve HTTP response times
  and avoid congestion of the Internet or other networks.