Isn't it funny how you can use a Spanish term many times and never stop to think how you would say it in English? "Equipo decanal" is such a case for me.

In the Spanish faculty where I worked, the equipo decanal consisted of the Dean, the Vice-Deans (I think there were two) and the Faculty (Academic) Secretary. However, I wouldn't guarantee that all equipos decanales are made up exactly like this.

What is certain, however, is that the equipo decanal consists of the academics who are elected together as a team of candidates, and does not include the administrative and secretarial staff who assist them.

I agree that "Dean's team" just doesn't sound right. It's quite true, as Laura says, that in the US and the UK faculties are usually run by the Dean's Office. The trouble is that the Dean's Office consists not only of the Dean, Vice-Deans and Faculty Secretary but also the support staff. You can't call the equipo decanal the Dean's Office or the Dean's Office staff, because those that are empowered to interpret the regulations in your doc. are just the academics in the Dean's Office, those elected to office by the faculty, not the support staff in the Dean's Office.

One solution would be to spell it out: "the Dean, the Vice-Deans and the Faculty Secretary", but we can't be sure exactly who is involved. So I'd go for the term "Faculty Executive Team" which is used in a number of British universities and refers precisely to the Dean and his/her executive team of academics (Vice-Deans or Assistant Deans etc.).

Here's an example from UCL; there are a number of others:

"The Vice-Deans are responsible to the Dean and together with the other Vice-Deans, Directors of Divisions and Institutes, Faculty Tutor and the Faculty Manager comprise the Faculty Executive Team."
http://www.ucl.ac.uk/slms/vacancies/ViceDeanforEducationJD

For comparison, here's a page on an equipo decanal at UAM:
http://www.uam.es/ss/Satellite/FilosofiayLetras/es/123488998...

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Note added at 1 hr (2014-05-21 18:43:34 GMT)
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To put it in Spanish university terms, the equipo decanal consists exclusively of PDI (personal docente e investigador), whereas the Dean's Office Staff comprises a combination of PDI and PAS (personal de administración y servicios). PDI and PAS is the great divide of Spanish university life, affecting everything from your salary regime to where you go for your coffee break. It would definitely be out of the question for PAS to interpret and take decisions on the regulations.