Galaxy Flyer,
Phase III. Phase III began April 28, 1994, when the first instrument approach procedures were published to include “or GPS” in the title of the published approach procedure. Neither the aircraft traditional avionics nor the underlying ground station navaid(s) need be installed, operational, or monitored to fly the nonprecision approaches at the destination airport. For GPS systems that do not use RAIM for integrity, the ground-based navaid(s) and the airborne avionics that provide the equivalent integrity must be installed and operating during the approach. For any required alternate airport, the traditional ground-based and airborne navigational equipment that defines the instrument approach procedure and route to the alternate must be installed and operational.
This statement in bold is true as long as you have the "or GPS" on the plate.
AIM 1-32 paragraph 3 (2004)
The GPS Approach overlay Program is an authorization for pilots to use GPS avionics under IFR for flying designated nonprecision instrument approach procedures, except LOC, LDA and simplified directional facility (SDF) procedures. These procedures are now identified by the name of the procedure and “or GPS” (eg., VOR/DME or GPS RWY 15). Other previous types of overlays have either been converted to this format or replaced with stand-alone procedures. Only approaches contained in the current onboard navigation database are authorized. The navigation database may contain information about nonoverlay approach procedures that is intended to be used to enhance position orientation, generally by providing a map, while flying these approaches using conventional NAVAIDS. This approach information should not be confused with GPS overlay approach (see the receiver operating manual, AFM, or AFM supplement for details on how to identify these approaches in the navigation database.
Glad to here if something has changed in the US since then.
I am sure your airplanes are capable of doing many many things, but this is not the issue here.
Again I would be very glad to know which eu countries permit to fly a conventional VOR/DME approach when the radionavaid is unserviceable...