I'm a newbie to Frequent Flyer programs so forgive if this sounds ignorant.

Hypothetically, say I am enrolled in two different FFlyer programs (take your pick), say Air France and United. And let's say both of them partner with Hyatt hotels and give you 500 miles if you stay there. So if I were to check into a Hyatt hotel, would i be earning for BOTH flyer programs or just one? Please help. Thanks!!