When Eta took up arms 50 years ago in pursuit of an independent Basque homeland, Spain was an international pariah in the grip of Franco's dictatorship. The Basque language was banned and political parties were illegal.

Many considered it reasonable, even inevitable, that Basque political opposition should take the form of armed attacks on military targets: Eta's first armed action was the derailment of a troop train near Bilbao.

Exactly half a century on, Spain is a sturdy democracy and the Basque country enjoys more autonomy than any other region in Europe, but for the armed separatists little has changed. They still want to be free of Spain and to achieve full independence.

They are still planting bombs and firing pistols, and funerals of civil guardsmen are still being held, such as that at Palma Cathedral in Mallorca on Friday for Carlos Saenz de Tejadá and Diego Salva de Lezaun, who were killed by a car bomb on Thursday in the island's tourist town of Palmanova.

Europe's last armed separatist organisation survived Spain's social and political transformation with its military structure, its armed tactics and revolutionary ideology intact. To the bafflement of the rest of Europe, and the grief of those who continue to mourn their dead, Eta dismisses Spain's democratic institutions as the mere window-dressing of an eternally oppressive state.

Prince Felipe and Princess Letizia attended the joint funeral of the dead officers. King Juan Carlos is due to arrive in Mallorca next week for his annual holiday, adding to the security jitters. Spain's royal family has a summer palace just six miles away at Cala Major, where the king was targeted in a failed Eta attack in 1995.

But more baffling than the separatists' unresponsiveness to changing times is the inability of Spain's security services to defeat or seriously weaken them, despite superior intelligence and vital co-operation from France.

Spaniards have been assured for decades that Eta was on the brink of surrender or defeat. Such statements have come to be an essential part of the anti-terrorist rhetoric. But every time a top Eta leader is arrested (four in the past year) the organisation seems able to mount a spectacular armed riposte.

Security forces on the island remained on maximum alert this weekend. Police say they believe the terrorists are still "holed up in an apartment" on Mallorca. Photographs of six suspects were circulated. For tourists, "maximum alert" translates as maximum inconvenience at airports.

Thursday's bomb attack came a day after another blast injured scores of people in Burgos, in the north of the Spanish mainland, and this double-whammy was the most dramatic show of Eta force for years. Officials suspect the operation was designed as a violent celebration of the organisation's anniversary. Unusually, no warning was given before the attack, signalling a steelier approach.

Whatever the motive, the attacks reveal how Eta's tactics have evolved over the decades: not only did terrorists target armed agents of the Spanish state, they also chose their place and time – one of Europe's top tourist destinations – with an eye to the maximum propaganda effect. Eta's summer terror campaigns in Spanish resorts have become a regular feature of recent years, drawing international attention and highlighting the authorities' helplessness.

Once again, tourists across Europe will be worrying if their Mediterranean break will be safe. Eta warned recently that it would resume a campaign against coastal holiday targets. Should we take these warnings at face value?

Prime minister José Luis Rodríguez Zapatero insists every effort is being made to catch "these vile murderers" but his words will fail to convince a traumatised nation. Every time Eta has been thrown on to the defensive it has come back with a violent response.

Zapatero's socialist government, like its predecessors, has tried everything from the carrot to the cosh to solve the separatist conflict. Yet, socially isolated but for a fanatical hard core, commanded by younger, less experienced and harder-line militants, Eta at 50 remains fully operative.