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Ananoman
you are not exactly correct, you only have to choose an alternate that has an approach that does not require gps if the destination airport only has approaches that will require a gps for your airplane. So as by your example, In an airplane that is using a GPS in lieu of DME of NDB information, If the destination airport has for instance an ILS or a VOR approach that does not require DME or an ADF, then you can file as an alternate an airport that you will be required to use a GPS for an approach, whether that be a GPS approach or an approach requiring DME or an ADF. The reason for that alternate rule is so if there is a RAIM problem, you will be able to fly an approach to put the airplane on the ground without the GPS, but if your destination airport does not require a GPS then your alternate can. So basically one of your filed destination airports primary or alternate must have an approach that does not require a GPS, that does not mean you cannot fly an approach that requires a GPS at both of those airports, it just means that one of them must have an approach that doen't require a GPS.
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Your position is not supported by the AIM. AIM 1-1-20 list the requirements for GPS IFR operations. It also spells out the requirements to use GPS in lieu of ADF and DME. Nowhere does it say that you only have to have an alternate that does not rely on GPS if the approaches at your destination require the use of GPS. It does however state that: "A non-GPS approach procedure must exist at the alternate airport when one is required. If the non-GPS approaches on which the pilot must rely require DME or ADF, the aircraft must be equipped with DME or ADF avionics as appropriate." As far as I know, there are no exceptions to this rule. I also do not know of any airports that have only stand alone GPS approaches that are approved for use as an alternate.
Usually this is not an issue. If you need an alternate you can usually find one that has ILS or VOR approaches that do not require ADF or DME. However, if you are flying in bad weather and need a precision alternate, it can be problematic when the closest ILS list "ADF or DME required".