If the space between the two doorframes is more than four tefachim, you would need two mezuzot: The area between the two doors has the special status of a beit sha’ar (gate-house) and thus needs a mezuzah even though it is not four by four amot sq.
If the space is less than four tefachim, a mezuzah should be put on the inner doorframe. The security door needs no mezuzah since the area it encloses is too small to be considered a beit sha’ar. 
[See also question “Two Doors Sharing the Same Doorway.”]
 Agur B’ohalecha 36:40.