Is this transparent background a Sprite Object or a layer with its Opacity turned on?
Either way you can set a variable to check if the BG should fade or not and if yes, add to its opacity a value multiplied by dt.
On the Sprite object it should look like this:
isFading---> set Sprite Opacity to self.Opacity + (a value) * dt
This will gradually add (a value) to the spite's opacity until it it reaches 100 (it' cant go any higher).
The same applies if the opacity values that you want to alter are on a opaque layer, the difference is that you'll get the layer's opacity actions on the system actions.
If you can clarify what is it that you want to fade I can make you an example capx...