In that case, even if the space between them is more than four tefachim, only one mezuzah is necessary. The inner door should get the mezuzah: Since it opens onto a large room, it has a clear Torah obligation, whereas the obligation of a small beit sha’ar may be Rabbinic when it has no purpose other than as a passageway. 
However, if the space between the doors has a distinct purpose, such as a storage area, a second mezuzah should be affixed on the outside door, without a berachah. 
Even if the inner door only has space for a mezuzah on the outside of its post, since the mezuzah is within the doorway and under the lintel, it may face forward.
[See also question “Security gate in front of door.”]
 Agur B’ohalecha 36:41.
 Agur B’ohalecha 36:41:79. Additional examples of a distinct purpose include if the space is used as a position for a security guard to stand or as an area to unload goods.