One arrest was made close to Madrid, the others in various Moroccan cities.
Those arrested are suspected of involvement in a network to send fighters to areas of Syria and Iraq under ISIS control.
On August 21, a Moroccan who had lived in Spain was arrested following a foiled attack on a high-speed French train.
Ayoub El-Khazzani, 25, originally from Tetouan in northern Morocco, arrived in Spain in 2007 and lived there for seven years, in Madrid and Algeciras, before moving to France.
He is suspected of having had contact with radical Islamists and had been put on a list marked as “potentially dangerous” by Spanish authorities. They flagged this up to French counterparts in February 2014.
Spanish counter-terrorism sources quoted on August 24 by the Spanish Cadena Ser radio network said that some 800 people with a radical Islamist profile were in Europe and ready to strike, having returned from Syria and Iraq.
The latest Spanish arrest took place in San Martin de la Vega, close to Madrid, and the others were in the Moroccan cities of Fez, Casablanca, Nador, al-Hoceima and Driouech.
The Spanish interior ministry said the operation was ongoing, without giving specific details.
In June, Spain raised the terrorism threat level from three to four out of a possible five, increasing the number of armed police at sensitive sites across the country.
Level four means the intelligence services believe there is a high risk of a terror attack happening.
Both Spain and Morocco have arrested dozens of suspected radical Islamists in recent years.
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