ASP.Net Session Problems, Possible Session Swapping

I have an ASP.Net 1.1 application that is having a problem with the session variables swapping with simultaneous users.  I am storing static variables which I though were only accessible to the current user.  But I think they may be shared by all users across sessions  Is this possible? Could this be why I seem to have session swapping?

  private void Page_Load(object sender, System.EventArgs e)
  {
    if (!Page.IsPostBack)
    {
        Invitee.ID = Convert.ToInt32(Session["InviteeID"].ToString());
    }
  }  

public class Invitee
{
  public static int ID;
  public static string Name;
}

Thanks,
- JP