In 1978, Quinta das Águas Livres in Sintra was acquired and the construction works of the infrastructures necessary to organise the instruction activities and to accommodate the distinct elements that would form a future operational group began.

Alongside, also began studies regarding the creation of the GOE and, with the co-operation of the British government, thanks to the efforts of Mota Pinto's government, elements of the 22nd Special Air Service Regiment (SAS) came to Portugal to train and start the formation of a police group able to conduct anti-terrorist missions.

GOE's capabilities were put to the test in June, 1983, when Armenian commandos, using rented cars, invaded the residence of the Turkish ambassador and wounded a PSP officer who was part of the embassy's security team, holding the rest of the people there hostage.

After 1991, GOE operational elements, together with ex-operators, began missions of protection of diplomatic representatives and installations in foreign countries where there are unstable situations or armed conflicts.

GOE also intervenes if the evacuation of Portuguese citizens is needed: in 1992 in Luanda (Angola), in 1991 and 1997 in the Democratic Republic of the Congo (former Zaire) and in other countries like Guinea-Bissau, Algeria, Macau, Bosnia and, in 2011, in Egypt.