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Open thread in foreach loop
foreach (System.Messaging.Message m in msgs)
{
    byte[] bytes = new byte[m.BodyStream.Length];
    m.BodyStream.Read(bytes, 0, (int)m.BodyStream.Length);
    System.Text.ASCIIEncoding ascii = new System.Text.ASCIIEncoding();

    ParserClass tst = new ParserClass(ascii.GetString(bytes, 0, (int)m.BodyStream.Length));
    new Thread( new ThreadStart(tst.ProcessXML)).Start();
}

private static object thLockMe = new object();
public string xmlString { get; set; }

public ParserClass(string xmlStringObj)
{
    this.xmlString = xmlStringObj;
}

public void ProcessXML()
{
    lock (thLockMe)
    {
        XDocument reader = XDocument.Parse(xmlString);
        //Some more code...
    }
}

foreach (System.Messaging.Message m in msgs)
{
    byte[] bytes = new byte[m.BodyStream.Length];
    m.BodyStream.Read(bytes, 0, (int)m.BodyStream.Length);
    System.Text.ASCIIEncoding ascii = new System.Text.ASCIIEncoding();

    ParserClass tst = new ParserClass(ascii.GetString(bytes, 0, (int)m.BodyStream.Length));
    ThreadPool.QueueUserWorkItem(x => tst.ProcessXML());
}

private static object thLockMe = new object();
public string XmlString { get; set; }

public ParserClass(string xmlString)
{
    XmlString = xmlString;
}

public void ProcessXML()
{
    XDocument reader = XDocument.Parse(xmlString);
    // some more code which doesn't need to access the shared resource

    lock (thLockMe)
    {
        // the necessary code to access the shared resource (and only that)
    }

    // more code
}