C#

private void geraGzipToolStripMenuItem1_Click(object sender, EventArgs e)
{
    XmlDocument doc = new XmlDocument();
    doc.LoadXml("<teste><dirso>ama posa</dirso></teste>");
    FileStream f = new FileStream("C:\\DADOS\\JR\\JRFW\\bin\\output\\read.xml.gz",
        FileMode.OpenOrCreate, FileAccess.Write);
    GZipEx gz = new GZipEx();
    gz.EncodeXml(doc, f);
}

public void EncodeXml(XmlDocument xml, Stream streamOut)
{
    Stream m = new MemoryStream();
    xml.Save(m);
    EncodeStream(m, streamOut);
    xml.Save("C:\\DADOS\\JR\\JRFW\\bin\\output\\teste.xml");
}

public void EncodeStream(Stream streamIn, Stream streamOut)
{
    GZipOutputStream gz = new GZipOutputStream(streamOut);
    byte[] btout = new byte[bufferSize];
    int nRead;
    while ((nRead = streamIn.Read(btout, 0, bufferSize)) > 0)
    {
        gz.Write(btout, 0, nRead);
    }
    gz.Flush();
    gz.Close();
    streamOut.Close();
}