bw1.RunWorkerCompleted += new RunWorkerCompletedEventHandler(bw1_RunWorkerCompleted);

private void bw1_RunWorkerCompleted(object sender, RunWorkerCompletedEventArgs e)
{
    //celebration!

    //and then start the 2nd BackgroundWorker
    BackgroundWorker bw2 = new BackgroundWorker();
    bw2.DoWork += new DoWorkEventHandler(bw2_DoWork);
    bw2.RunWorkerCompleted += new RunWorkerCompletedEventHandler(bw2_RunWorkerCompleted);
    bw2.RunWorkerAsync();
}