The whirl-flutter problem of an advanced turboprop configuration with two pusher propellers positioned at the aircraft fuselage cone is analyzed. Coupling between the two propellers and the flexible backup structure— pylons and aft fuselage cone—is allowed. Very interesting results lead to the conclusion that, for typical stiffness ratios between the backup structure and the engine suspension system, a special type of flutter involving mainly the backup structure may be dominant over traditional propeller-nacelle whirl flutter. This type of flutter is solely due to the propeller whirl and may be critical either in some modern configurations of aircrafts (as propfans) or in new conceptions of power plants installations employing additional vibration insulators at the pylon-fuselage attachments.