It is possible that the server you are visiting is sending "redirect" headers.

Check out the $mech->redirect_ok() option, which instructs your virtual browser (WWW::Mechanize) to follow redirects.

update 1: a simpler approach may be to parse the header yourself looking for a URI to follow. Try the following on one of your magically redirecting pages:

  use WWW::Mechanize;

  my $mech = WWW::Mechanize->new( quiet => 1 );
  $mech->get( "http://www.mysite.com/index.html" );
  die( "Error getting page" ) if ( ! $mech->success() );
  print( $mech->response->headers_as_string );
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or alternatively if you want to see the entire message, headers included, for debugging purposes, replace ->headers_as_string with ->as_string..