Image copyright AFP Image caption Juergen Kantner and Sabine Merz had been abducted before - off Somalia in 2008 
 
 Islamic militants in the Philippines have posted a video showing the beheading of a German hostage. 
 
 Juergen Kantner was abducted from his yacht off Malaysia's Sabah state in November. His companion Sabine Merz's body was later found on the boat. 
 
 A deadline for a 30m peso (£483,000; $600,000) ransom expired on Sunday. 
 
 Mr Kantner, 70, and Ms Merz had been abducted before. They were held for 52 days in 2008 by Somali pirates and were released after a ransom was paid. 
 
 The video, reported by the SITE militancy-monitoring group, shows Mr Kantner being killed by a knife-wielding man. 
 
 Government envoy Jesus Dureza confirmed the killing. 
 
 "Up to the last moment, many sectors, including the armed forces, exhausted all efforts to save his life. We all tried our best but to no avail," he said. 
 
 Abu Sayyaf is one of the smallest and most violent jihadist groups in the southern Philippines, known for its brutality, including beheadings. 
 
 It has pledged allegiance to so-called Islamic State and has carried out kidnappings of foreigners and Filipinos. Some have been released for ransoms but a number are still being held. 
 
 Who are Abu Sayyaf? 
 
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 The German foreign ministry said in a statement that there was no longer any reasonable doubt that the German abducted in the Philippines was dead. 
 
 "We are deeply shocked by the inhuman and gruesome act," it added. 
 
 A Philippine police report said Mr Kantner had been killed in the Indanan area of southern Sulu province on Sunday afternoon. 
 
 However, no body has yet been recovered. 
 
 The Philippine military had carried out air strikes on Abu Sayyaf positions in Sulu over the weekend as the deadline approached. 
 
 After the German couple's yacht, the Rockall, was found off Laparan Island in Sulu province on 7 November, Abu Sayyaf had issued an audio message saying it was responsible for the abduction. 
 
 Sulu - the home of Philippine militancy 
 
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 Ms Merz was apparently killed as she tried to resist the militants. 
 
 Analysis: Damien McGuinness, BBC News, Berlin 
 
 A year after Juergen Kantner was kidnapped off the coast of Somalia in 2008 he returned - to pick up his yacht and to carry on sailing in the region. 
 
 This decision, and the second abduction in November, sparked a debate in Germany about the extent to which individuals have a responsibility to avoid danger. 
 
 Commentators discussed whether it was brave or reckless to go sailing in some of the world's most dangerous seas that were plagued by pirates - particularly given that the German government had reportedly paid huge sums in ransom to release Mr Kantner and his partner the first time they were abducted. 
 
 But Mr Kantner justified his decision by saying that after 32 years on his boat he had no friends left in Germany, and that everything he owned was on his yacht. 
 
 "My boat is my life and I don't want to lose it," he said at the time. "I want to live and die sailing." ||||| The Philippine Daily Inquirer quoted a spokesman for Abu Sayyaf as saying via telephone that the woman had fired upon them. “Our men shot back and killed her,” he said. 
 
 The newspaper said that the spokesman had made a man come to the phone and that he had identified himself as Jürgen Kantner. The account quoted him as saying: “Pirates took our boat and they took us.” 
 
 In Berlin, the foreign ministry said it was working with Philippine authorities to clarify the situation. “As always in such cases, I would like to be very tight-lipped,” said the ministry spokesman, Martin Schäfer. He stressed that there was no confirmation of the reported killing or the abduction. 
 
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 Uwe Janssen, editor in chief of the German yachting website, Yacht.de, noted the lack of official confirmation but wrote that a photograph released by the Philippine military authorities “is clear: the attacked vessel indeed belongs to Jürgen Kantner.” 
 
 The sailboat in the photo is marked Rockall, the same name that was on the vessel captured by the Somalis eight years ago. 
 
 Mr. Janssen said, “Everything suggests that the two victims” were Mr. Kantner and Ms. Merz. 
 
 In May 2009, Agence France-Presse reported that Mr. Kantner had returned to Somalia after the couple’s abduction and release, and quoted him as vowing to get the Rockall seaworthy once more and to set off for Asia. 
 
 “Why should I return to Germany, where I have nobody?” he was quoted as saying. “After 32 years on my boat, I have lost all contact with them.” He acknowledged “that it is a little bit like suicide,” and said he prayed that he would not get captured a second time. 
 
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 In a lengthy interview with the German magazine Yacht after the 2008 abduction, Mr. Kantner and Ms. Merz said they had been captured then while sailing close to the coast of Yemen, and that they had no warning of special danger. They dismissed suggestions that they had courted danger, citing cases of vessels robbed in calmer regions, like the Canary Islands or Corsica.
– A German couple who's spent four decades sailing the world has apparently been abducted by pirates for a second time, with what appears to be a fatal result. Jürgen Kantner and Sabine Merz—who were held by Somali pirates for 52 days in 2008, until a six-figure ransom was reportedly paid—were seized by Abu Sayyaf militants in the southern Philippines on Saturday, the New York Times reports. Merz fired at the militants, and "our men shot back and killed her," an Abu Sayyaf spokesman told the Philippine Daily Inquirer over the phone. A man who identified himself as Kantner then came on the line claiming, "pirates took our boat and they took us." Abu Sayyaf militants also killed two Canadians earlier this year. The German Foreign Ministry says it's investigating the reports but hasn't confirmed the abduction or Merz's death. However, the Philippine military released a photo of the attacked boat, recovered on Sunday, which shows it to be the same 30-foot yacht, dubbed the Rockall, that was seized by pirates in 2008. A military rep says a woman's naked body was also found on board bearing "gunshot wounds" and signs of a sexual assault. "A shotgun was also recovered beside the woman's body," the rep says. A year after their first abduction, Kantner told the AFP that he would keep sailing, but "I pray to God that pirates won't get me again. Of course, buying a gun is an option." (An American man was held for 18 days by Dolly Parton-loving pirates.)