I doubt that there is a linear progression between combat operations and stablization ops, which is what Rank Amateur(RA) seems to be advocating, and what Ken White (KW) seems to be denying. However, I also think KW's assertion that both are occurring simultaneously is not completely accurate. Rob's point about stability seems very much on the mark. It is probably more correct to say that combat ops and stablilzation ops are two sides of the same coin (no pun intended here), which have a goal of maintaining or restoring stability (also known as peace in some circles).

For some reason, I seem to be infected with medical metaphors at present. I am not a doctor nor have I played one on TV. But I have stayed in Holiday Inns.
Doctors both stabilize patients and treat patients, often, but not always, simultaneously, and often, but not always, using different procedures. One goal of patient stablization is to try to ensure that they don't die on the table while the docs are trying to treat the cause of the problem--for example, they keep pumping blood into the patient (stablization) while they are figuring out which artery has been cut and then suture it back together (kinetic intervention or treatment). Sometimes however, I suspect that stablizaing the patient is also treatment--as when aspirin is administered to a person with a fever. Maybe I'm applying the wrong analogy, but it sure seems to me that peace is the political analogue to biological health.

By the way, for those who hold to the linear process model, stablilization need not be the last step in the process. I suspect it also applies in Phase 0 of any operation as a means of trying to avoid have to make a major commitment to kinetic operations (AKA putting a lot of boots on the ground/aircraft in the sky and having them release a lot of metal from their various bullet throwers, bomb bays, and wing pylons at what are probably poorly discriminable targets). Also, I suspect that you can do stablization at home as well as in foreign countries--Guard missions that include post hurricane relief ops to New Orleans, guarding civil rights marchers on their way to Selma, and patrolling the streets of Watts after "race riots" come to mind as examples.